Question 1: Palette 1/116

Objective Physics Vol-1 MCQ

A scooter is moving along a straight line $AB$ covers a distance of $360\text{ m}$ in $24\text{ s}$ and returns back from $B$ to $C$ and covers $240\text{ m}$ in $18\text{ s}$. Find the total distance travelled by the scooter.

A

$120\text{ m}$

B

$600\text{ m}$

C

$360\text{ m}$

D

$240\text{ m}$

Question 2: Palette 2/116

Objective Physics Vol-1 MCQ

A wheel completes $2000\text{ revolutions}$ to cover the $9.5\text{ km}$ distance. Find the diameter of the wheel.

A

$1.51\text{ m}$

B

$3.02\text{ m}$

C

$0.75\text{ m}$

D

$2.14\text{ m}$

Question 3: Palette 3/116

Objective Physics Vol-1 MCQ

A man starts from his home and walks $50\text{ m}$ towards north, then he turns towards east and walks $40\text{ m}$ and then reaches to his office after moving $20\text{ m}$ towards south. What is the total distance covered by the man from his home to office and what is his displacement from his home to office?

A

Distance = $110\text{ m}$, Displacement = $50\text{ m}$

B

Distance = $50\text{ m}$, Displacement = $110\text{ m}$

C

Distance = $110\text{ m}$, Displacement = $70\text{ m}$

D

Distance = $70\text{ m}$, Displacement = $50\text{ m}$

Question 4: Palette 4/116

Objective Physics Vol-1 MCQ

An object covers $1/4\text{th}$ of a circular path of radius $r$. What will be the ratio of the distance and displacement of the object?

A

$\frac{\pi}{2\sqrt{2}}$

B

$\frac{\pi}{\sqrt{2}}$

C

$\frac{2\sqrt{2}}{\pi}$

D

$\frac{\pi}{4}$

Question 5: Palette 5/116

Objective Physics Vol-1 MCQ

Displacement of a person moving from $X$ to $Y$ along a semicircular path of radius $r$ is $200\text{ m}$. What is the distance travelled by him?

A

$200\text{ m}$

B

$100\pi\text{ m}$

C

$400\text{ m}$

D

$200\pi\text{ m}$

Question 6: Palette 6/116

Objective Physics Vol-1 MCQ

An athlete completes one round of a circular track of diameter $200\text{ m}$ in $40\text{ s}$. What will be the distance covered and the displacement at the end of $2\text{ min } 20\text{ s}$?

A

Distance = $2200\text{ m}$, Displacement = $200\text{ m}$

B

Distance = $200\text{ m}$, Displacement = $2200\text{ m}$

C

Distance = $4400\text{ m}$, Displacement = $100\text{ m}$

D

Distance = $2200\text{ m}$, Displacement = $0\text{ m}$

Question 7: Palette 7/116

Objective Physics Vol-1 MCQ

Which of the following is a one-dimensional motion?

A

Landing of an aircraft

B

Earth revolving around the sun

C

Motion of wheels of moving train

D

Train running on a straight track

Question 8: Palette 8/116

Objective Physics Vol-1 MCQ

A person moves towards east for $3\text{ m}$, then towards north for $4\text{ m}$ and then moves upwards for $5\text{ m}$. What is his distance now from the starting point?

A

$10\text{ m}$

B

$12\text{ m}$

C

$5\sqrt{2}\text{ m}$

D

$5\text{ m}$

Question 9: Palette 9/116

Objective Physics Vol-1 MCQ

A particle moves in a circle of radius $R$ from $A$ to $B$ as shown in figure. The distance covered by the object is

A

$\frac{\pi R}{3}$

B

$\frac{\pi R}{2}$

C

$\frac{\pi R}{4}$

D

$\pi R$

Question 10: Palette 10/116

Objective Physics Vol-1 MCQ

A wheel of radius $1\text{ m}$ rolls forward half a revolution on a horizontal ground. The magnitude of displacement of the point of the wheel initially in contact with the ground is

A

$2\pi$

B

$\sqrt{2}\pi$

C

$\sqrt{\pi^2 + 4}$

D

$\pi$

Question 11: Palette 11/116

Objective Physics Vol-1 MCQ

The three initial and final positions of a man on the x-axis are given as:
(i) $(-8\text{ m}, 7\text{ m})$
(ii) $(7\text{ m}, -3\text{ m})$
(iii) $(-7\text{ m}, 3\text{ m})$
Which pair gives the negative displacement?

A

(i)

B

(ii)

C

(iii)

D

(i) and (iii)

Question 12: Palette 12/116

Objective Physics Vol-1 MCQ

The numerical ratio of displacement to the distance for a moving object is always

A

less than one

B

equal to one

C

equal to or less than one

D

equal to or greater than one

Question 13: Palette 13/116

Objective Physics Vol-1 MCQ

A particle moves along a circular path of radius $r$. The distance and displacement of the particle after half a revolution is

A

$0, 2\pi r$

B

$2\pi r, 0$

C

$0, \pi r$

D

$\pi r, 0$

Question 14: Palette 14/116

Objective Physics Vol-1 MCQ

A particle starts from the origin, goes along $X$-axis to the point $(20\text{ m}, 0)$ and then returns along the same line to the point $(-20\text{ m}, 0)$. The distance and displacement of the particle during the trip are

A

$40\text{ m}, 0$

B

$40\text{ m}, -20\text{ m}$

C

$60\text{ m}, -20\text{ m}$

D

$40\text{ m}, 20\text{ m}$

Question 15: Palette 15/116

Objective Physics Vol-1 MCQ

Abdul while driving to school computes the average speed for his trip to be $20\text{ km h}^{-1}$. On his return trip along the same route, there is less traffic and the average speed is $40\text{ km h}^{-1}$. What is the average speed for Abdul's trip?

A

$30.5\text{ km h}^{-1}$

B

$26.67\text{ km h}^{-1}$

C

$24.5\text{ km h}^{-1}$

D

$32.0\text{ km h}^{-1}$

Question 16: Palette 16/116

Objective Physics Vol-1 MCQ

A car covers the first half of the distance between two places at a speed of $40\text{ km h}^{-1}$ and second half at $60\text{ km h}^{-1}$. Calculate the average speed of the car.

A

$52\text{ km h}^{-1}$

B

$45\text{ km h}^{-1}$

C

$48\text{ km h}^{-1}$

D

$50\text{ km h}^{-1}$

Question 17: Palette 17/116

Objective Physics Vol-1 MCQ

A car moves from $X$ to $Y$ with a uniform speed $v_u$ and returns to $X$ with a uniform speed $v_d$. Find average speed for this round trip.

A

$\frac{v_u v_d}{v_u + v_d}$

B

$\frac{3v_u v_d}{v_u + v_d}$

C

$\frac{2v_u v_d}{v_u + v_d}$

D

$\frac{v_u + v_d}{2v_u v_d}$

Question 18: Palette 18/116

Objective Physics Vol-1 MCQ

A particle travelled half the distance with a speed $v_0$. The remaining part of the distance was covered with speed $v_1$ for half the time and with speed $v_2$ for the other half of the time. Find the average speed of the particle.

A

$\frac{2v_0(v_1 + v_2)}{v_1 + v_2 + v_0}$

B

$\frac{2v_0(v_1 + v_2)}{v_1 + v_2 + 2v_0}$

C

$\frac{v_0(v_1 + v_2)}{2(v_1 + v_2 + v_0)}$

D

$\frac{v_0(v_1 + v_2)}{v_1 + v_2 + v_0}$

Question 19: Palette 19/116

Objective Physics Vol-1 MCQ

In one second, a particle goes from point $A$ to point $B$ moving in a semicircular path as shown in figure. Find the magnitude of average velocity.

A

$1.5\text{ ms}^{-1}$

B

$2.5\text{ ms}^{-1}$

C

$2\text{ ms}^{-1}$

D

$3\text{ ms}^{-1}$

Question 20: Palette 20/116

Objective Physics Vol-1 MCQ

A farmer has to go $500\text{ m}$ due north, $400\text{ m}$ due east and $200\text{ m}$ due south to reach his field. If he takes $20\text{ min}$ to reach the field, (i) what distance has he to walk to reach the field? (ii) what is the displacement from his house to the field? (iii) what is the average speed of farmer during the walk? (iv) what is the average velocity of farmer during the walk? [Note: This question specifically focuses on finding the total distance and magnitude of displacement.]

A

Distance: $1100\text{ m}$, Displacement: $500\text{ m}$

B

Distance: $1000\text{ m}$, Displacement: $400\text{ m}$

C

Distance: $1100\text{ m}$, Displacement: $600\text{ m}$

D

Distance: $900\text{ m}$, Displacement: $500\text{ m}$

Question 21: Palette 21/116

Objective Physics Vol-1 MCQ

Joseph jogs from one end $A$ to the other end $B$ of a straight $300\text{ m}$ road in $2\text{ min } 50\text{ s}$ and then turns around and jogs $100\text{ m}$ back to point $C$ in another $1\text{ min}$. What are Joseph's average speeds and velocities in jogging (i) from $A$ to $B$ and (ii) from $A$ to $C$?

A

Average speed from $A$ to $B$ is $1.76\text{ ms}^{-1}$, average velocity from $A$ to $B$ is $1.76\text{ ms}^{-1}$; Average speed from $A$ to $C$ is $1.74\text{ ms}^{-1}$, average velocity from $A$ to $C$ is $0.87\text{ ms}^{-1}$

B

Average speed from $A$ to $B$ is $1.50\text{ ms}^{-1}$, average velocity from $A$ to $B$ is $1.50\text{ ms}^{-1}$; Average speed from $A$ to $C$ is $1.20\text{ ms}^{-1}$, average velocity from $A$ to $C$ is $0.50\text{ ms}^{-1}$

C

Average speed from $A$ to $B$ is $2.00\text{ ms}^{-1}$, average velocity from $A$ to $B$ is $2.00\text{ ms}^{-1}$; Average speed from $A$ to $C$ is $1.90\text{ ms}^{-1}$, average velocity from $A$ to $C$ is $1.10\text{ ms}^{-1}$

D

Average speed from $A$ to $B$ is $1.76\text{ ms}^{-1}$, average velocity from $A$ to $B$ is $1.76\text{ ms}^{-1}$; Average speed from $A$ to $C$ is $2.10\text{ ms}^{-1}$, average velocity from $A$ to $C$ is $1.50\text{ ms}^{-1}$

Question 22: Palette 22/116

Objective Physics Vol-1 MCQ

The position of an object moving along $X$-axis is given by $x = 3t - 4t^2 + t^3$, where $x$ is in metres and $t$ in seconds. Find the position of the object at $t = 2\text{ s}$ and $t = 4\text{ s}$. What is the object displacement between $t = 0\text{ s}$ and $t = 4\text{ s}$, and what is its average velocity for the time interval from $t = 2\text{ s}$ to $t = 4\text{ s}$?

A

$x_2 = -2\text{ m}$, $x_4 = 12\text{ m}$, Displacement = $12\text{ m}$, Average Velocity = $7\text{ ms}^{-1}$

B

$x_2 = 2\text{ m}$, $x_4 = 10\text{ m}$, Displacement = $10\text{ m}$, Average Velocity = $5\text{ ms}^{-1}$

C

$x_2 = -4\text{ m}$, $x_4 = 14\text{ m}$, Displacement = $14\text{ m}$, Average Velocity = $8\text{ ms}^{-1}$

D

$x_2 = -2\text{ m}$, $x_4 = 15\text{ m}$, Displacement = $15\text{ m}$, Average Velocity = $9\text{ ms}^{-1}$

Question 23: Palette 23/116

Objective Physics Vol-1 MCQ

A car has to cover the distance $60\text{ km}$. If half of the total time, it travels with speed $80\text{ km h}^{-1}$ and in rest half time, its speed becomes $40\text{ km h}^{-1}$, the average speed of car will be

A

$120\text{ km h}^{-1}$

B

$80\text{ km h}^{-1}$

C

$60\text{ km h}^{-1}$

D

$180\text{ km h}^{-1}$

Question 24: Palette 24/116

Objective Physics Vol-1 MCQ

During the first $18\text{ min}$ of a $60\text{ min}$ trip, a car has an average speed of $11\text{ m min}^{-1}$. What should be the average speed for remaining $42\text{ min}$, so that car is having an average speed of $21\text{ m min}^{-1}$ for the entire trip?

A

$25.3\text{ m min}^{-1}$

B

$29.2\text{ m min}^{-1}$

C

$31\text{ m min}^{-1}$

D

$35.6\text{ m min}^{-1}$

Question 25: Palette 25/116

Objective Physics Vol-1 MCQ

A man walks on a straight road from his home to a market $2.5\text{ km}$ away with a speed of $5\text{ km h}^{-1}$. Finding the market closed, he instantly turns and walks back home with a speed of $7.5\text{ km h}^{-1}$. The average speed of the man over the interval of time $0$ to $40\text{ min}$ is equal to

A

$5\text{ km h}^{-1}$

B

$\frac{25}{4}\text{ km h}^{-1}$

C

$\frac{30}{4}\text{ km h}^{-1}$

D

$\frac{45}{8}\text{ km h}^{-1}$

Question 26: Palette 26/116

Objective Physics Vol-1 MCQ

A particle is constrained to move on a straight line path. It returns to the starting point after $10\text{ s}$. The total distance covered by the particle during this time is $30\text{ m}$. Which of the following statements about the motion of the particle is true?

A

Displacement of the particle is zero

B

Average speed of the particle is $3\text{ ms}^{-1}$

C

Displacement of the particle is $30\text{ m}$

D

Both (a) and (b)

Question 27: Palette 27/116

Objective Physics Vol-1 MCQ

A $150\text{ m}$ long train is moving with a uniform velocity of $45\text{ km h}^{-1}$. The time taken by the train to cross a bridge of length $850\text{ m}$ is

A

$56\text{ s}$

B

$68\text{ s}$

C

$80\text{ s}$

D

$92\text{ s}$

Question 28: Palette 28/116

Objective Physics Vol-1 MCQ

An insect crawls a distance of $4\text{ m}$ along north in $10\text{ s}$ and then a distance of $3\text{ m}$ along east in $5\text{ s}$. The average velocity of the insect is

A

$\frac{7}{15}\text{ ms}^{-1}$

B

$\frac{1}{5}\text{ ms}^{-1}$

C

$\frac{1}{3}\text{ ms}^{-1}$

D

$\frac{4}{5}\text{ ms}^{-1}$

Question 29: Palette 29/116

Objective Physics Vol-1 MCQ

A particle traversed $\frac{3}{4}\text{th}$ of the circle of radius $R$ in time $t$. The magnitude of the average velocity of the particle in this time interval is

A

$\frac{\pi R}{t}$

B

$\frac{3\pi R}{2t}$

C

$\frac{R\sqrt{2}}{t}$

D

$\frac{R}{\sqrt{2}t}$

Question 30: Palette 30/116

Objective Physics Vol-1 MCQ

A boy is running over a circular track with uniform speed of $10\text{ ms}^{-1}$. What is the average velocity for movement of boy along semicircle (in $\text{ms}^{-1}$)?

A

$\frac{10}{\pi}$

B

$\frac{40}{\pi}$

C

$10$

D

$\frac{20}{\pi}$

Question 31: Palette 31/116

Objective Physics Vol-1 MCQ

A car starts from rest, attains a velocity of $18 \mathrm{kmh}^{-1}$ with an acceleration of $0.5 \mathrm{ms}^{-2}$, travels 4 km with this uniform velocity and then comes to halt with a uniform deceleration of $0.4 \mathrm{ms}^{-2}$. Calculate the total time of travel of the car.

A

812.5 s

B

802.5 s

C

822.5 s

D

832.5 s

Question 32: Palette 32/116

Objective Physics Vol-1 MCQ

Acceleration of a particle changes when

A

direction of velocity changes

B

magnitude of velocity changes

C

Both (a) and (b)

D

speed changes

Question 33: Palette 33/116

Objective Physics Vol-1 MCQ

If a particle moves with an acceleration, then which of the following can remain constant?

A

Both speed and velocity

B

Neither speed nor velocity

C

Only the velocity

D

Only the speed

Question 34: Palette 34/116

Objective Physics Vol-1 MCQ

The average velocity of a body moving with uniform acceleration travelling a distance of $3.06 \mathrm{m}$ is $0.34 \mathrm{ms}^{-1}$. If the change in velocity of the body is $0.18 \mathrm{ms}^{-1}$, then during this time, its uniform acceleration is

A

$0.01 \mathrm{ms}^{-2}$

B

$0.02 \mathrm{ms}^{-2}$

C

$0.03 \mathrm{ms}^{-2}$

D

$0.04 \mathrm{ms}^{-2}$

Question 35: Palette 35/116

Objective Physics Vol-1 MCQ

A car travelling with a velocity of $80 \mathrm{km/h}$ slowed down to $44 \mathrm{km/h}$ in $15 \mathrm{s}$. The retardation is

A

$0.67 \mathrm{ms}^{-2}$

B

$1 \mathrm{ms}^{-2}$

C

$1.25 \mathrm{ms}^{-2}$

D

$1.5 \mathrm{ms}^{-2}$

Question 36: Palette 36/116

Objective Physics Vol-1 MCQ

An object is moving along the path OABO with constant speed, then

A

the acceleration of the object while moving along the path OABO is zero

B

the acceleration of the object along the path OA and BO is zero

C

there must be some acceleration along the path AB

D

Both (b) and (c)

Question 37: Palette 37/116

Objective Physics Vol-1 MCQ

Two cars start off a race with velocities $2 \mathrm{ms}^{-1}$ and $4 \mathrm{ms}^{-1}$ and travel in a straight line with uniform accelerations $2 \mathrm{ms}^{-2}$ and $1 \mathrm{ms}^{-2}$, respectively. What is the length of the path, if they reach the final point at the same time?

A

12 m

B

24 m

C

36 m

D

48 m

Question 38: Palette 38/116

Objective Physics Vol-1 MCQ

A car was moving at a rate of $18 \mathrm{kmh}^{-1}$. When the brakes were applied, it comes to rest at a distance of 100 m. Calculate the retardation produced by the brakes.

A

$0.125 \mathrm{ms}^{-2}$

B

$0.250 \mathrm{ms}^{-2}$

C

$0.500 \mathrm{ms}^{-2}$

D

$1.000 \mathrm{ms}^{-2}$

Question 39: Palette 39/116

Objective Physics Vol-1 MCQ

Two cars are travelling towards each other on a straight road at velocities $10 \mathrm{ms}^{-1}$ and $12 \mathrm{ms}^{-1}$, respectively. When they are 150 m apart, both the drivers apply their brakes and each car decelerates at $2 \mathrm{ms}^{-2}$ until it stops. How far apart will they be when both of them come to rest?

A

61 m

B

75 m

C

89 m

D

100 m

Question 40: Palette 40/116

Objective Physics Vol-1 MCQ

A train travelling at $20 \mathrm{kmh}^{-1}$ is approaching a platform. A bird is sitting on a pole on the platform. When the train is at a distance of 2 km from the pole, brakes are applied which produce a uniform deceleration in it. At that instant, the bird flies towards the train at $60 \mathrm{kmh}^{-1}$ and after touching the nearest point on the train flies back to the pole and then flies towards the train and continues repeating itself. Calculate how much distance the bird covers before the train stops?

A

6 km

B

12 km

C

18 km

D

24 km

Question 41: Palette 41/116

Objective Physics Vol-1 MCQ

A particle starts with an initial velocity and passes successively over the two halves of a given distance with accelerations $a_1$ and $a_2$, respectively. The final velocity is the same as if the whole distance is covered with a uniform acceleration of

A

$\frac{a_1 - a_2}{2}$

B

$\frac{2a_1 a_2}{a_1 + a_2}$

C

$\frac{a_1 + a_2}{2}$

D

$\sqrt{a_1 a_2}$

Question 42: Palette 42/116

Objective Physics Vol-1 MCQ

In a car race, car A takes a time $t$ less than car B at the finish point and passes the finishing point with speed $v$ more than that of the car B. Assuming that both the cars start from rest and travel with constant accelerations $a_1$ and $a_2$ respectively, the correct relation is

A

$v = \sqrt{a_1 a_2}t$

B

$v = (a_1 + a_2)t$

C

$v = \sqrt{\frac{a_1}{a_2}}t$

D

$v = \frac{a_1 a_2}{t}$

Question 43: Palette 43/116

Objective Physics Vol-1 MCQ

A body starting from rest has an acceleration of $4 \mathrm{ms}^{-2}$. The distance travelled by it in the 5th second is

A

20 m

B

18 m

C

16 m

D

24 m

Question 44: Palette 44/116

Objective Physics Vol-1 MCQ

A particle starts from rest and moves under constant acceleration in a straight line. The ratio of displacements in successive seconds is

A

1:2:3:...

B

1:4:9:...

C

2:4:6:...

D

1:3:5:...

Question 45: Palette 45/116

Objective Physics Vol-1 MCQ

Velocity of a body moving along a straight line with uniform acceleration reduces by $\frac{3}{4}$ of its initial velocity in time $t_{0}$. The total time of motion of the body till its velocity becomes zero is

A

$\frac{4}{3}t_{0}$

B

$\frac{3}{2}t_{0}$

C

$\frac{5}{3}t_{0}$

D

$\frac{8}{3}t_{0}$

Question 46: Palette 46/116

Objective Physics Vol-1 MCQ

The displacement of a body in 8 s starting from rest with an acceleration of $20 \mathrm{cms}^{-2}$ is

A

$64 \mathrm{m}$

B

$64 \mathrm{cm}$

C

$640 \mathrm{cm}$

D

$0.064 \mathrm{m}$

Question 47: Palette 47/116

Objective Physics Vol-1 MCQ

The motion of a particle is described by the equation $v = at$. The distance travelled by the particle in the first 4 s is

A

$4a$

B

$12a$

C

$6a$

D

$8a$

Question 48: Palette 48/116

Objective Physics Vol-1 MCQ

A particle starts with a velocity of $2 \mathrm{ms}^{-1}$ and moves in a straight line with a retardation of $0.1 \mathrm{ms}^{-2}$. The first time at which the particle is 15 m from the starting point is

A

10 s

B

20 s

C

30 s

D

40 s

Question 49: Palette 49/116

Objective Physics Vol-1 MCQ

A particle starts from rest, accelerates at $2 \mathrm{ms}^{-2}$ for 10 s and then moves with constant speed of $20 \mathrm{ms}^{-1}$ for 30 s and then decelerates at $4 \mathrm{ms}^{-2}$ till it stops after next 5 s. What is the distance travelled by it?

A

750 m

B

800 m

C

700 m

D

850 m

Question 50: Palette 50/116

Objective Physics Vol-1 MCQ

A body is moving with uniform velocity of $8 \mathrm{ms}^{-1}$. When the body just crossed another body, the second one starts and moves with uniform acceleration of $4 \mathrm{ms}^{-2}$. The time after which two bodies meet, will be

A

2 s

B

4 s

C

6 s

D

8 s

Question 51: Palette 51/116

Objective Physics Vol-1 MCQ

Two bodies A and B start from rest from the same point with a uniform acceleration of $2 \mathrm{ms}^{-2}$. If B starts one second later, then the two bodies are separated at the end of the next second, by

A

1 m

B

2 m

C

3 m

D

4 m

Question 52: Palette 52/116

Objective Physics Vol-1 MCQ

A train accelerating uniformly from rest attains a maximum speed of $40 \mathrm{ms}^{-1}$ in 20 s. It travels at this speed for 20 s and is brought to rest by uniform retardation in further 40 s. What is the average velocity during this period?

A

$\frac{80}{3} \mathrm{ms}^{-1}$

B

$40 \mathrm{ms}^{-1}$

C

$25 \mathrm{ms}^{-1}$

D

$30 \mathrm{ms}^{-1}$

Question 53: Palette 53/116

Objective Physics Vol-1 MCQ

A particle starts from rest and traverses a distance $l$ with uniform acceleration, then moves uniformly over a further distance $2l$ and finally comes to rest after moving a further distance $3l$ under uniform retardation. Assuming entire motion to be rectilinear motion, the ratio of average speed over the journey to the maximum speed on its ways is

A

1/5

B

2/5

C

3/5

D

4/5

Question 54: Palette 54/116

Objective Physics Vol-1 MCQ

A body travelling with uniform acceleration crosses two points $A$ and $B$ with velocities $20 \mathrm{ms}^{-1}$ and $30 \mathrm{ms}^{-1}$, respectively. The speed of the body at mid-point of $A$ and $B$ is

A

$25 \mathrm{ms}^{-1}$

B

$25.5 \mathrm{ms}^{-1}$

C

$24 \mathrm{ms}^{-1}$

D

$10\sqrt{6} \mathrm{ms}^{-1}$

Question 55: Palette 55/116

Objective Physics Vol-1 MCQ

If a body starts from rest and travels 120 cm in the 6th second, then what is the acceleration?

A

$0.20 \mathrm{ms}^{-2}$

B

$0.027 \mathrm{ms}^{-2}$

C

$0.218 \mathrm{ms}^{-2}$

D

$0.03 \mathrm{ms}^{-2}$

Question 56: Palette 56/116

Objective Physics Vol-1 MCQ

A ball is thrown upwards from the top of a tower 40 m high with a velocity of 10 m/s. Find the time when it strikes the ground. (Take, $g = 10 \mathrm{m/s}^{2}$)

A

4 s

B

2 s

C

5 s

D

3 s

Question 57: Palette 57/116

Objective Physics Vol-1 MCQ

A rocket is fired vertically up from the ground with a resultant vertical acceleration of $10 \mathrm{ms}^{-2}$. The fuel is finished in 1 min and it continues to move up. What is the maximum height reached by the rocket? (Take, $g = 10 \mathrm{ms}^{-2}$)

A

18 km

B

54 km

C

36 km

D

72 km

Question 58: Palette 58/116

Objective Physics Vol-1 MCQ

A juggler throws balls into air. He throws one ball whenever the previous one is at its highest point. How high does the balls rise, if he throws $n$ balls each second? (Acceleration due to gravity is $g$)

A

$\frac{g}{n^{2}}$

B

$\frac{g}{2n^{2}}$

C

$\frac{g}{4n^{2}}$

D

$\frac{2g}{n^{2}}$

Question 59: Palette 59/116

Objective Physics Vol-1 MCQ

From an elevated point A, a stone is projected vertically upwards. When the stone reaches a distance $h$ below A, its velocity is double of what it was at a height $h$ above A. What is the greatest height attained by the stone?

A

$\frac{h}{3}$

B

$\frac{2h}{3}$

C

$\frac{4h}{3}$

D

$\frac{5h}{3}$

Question 60: Palette 60/116

Objective Physics Vol-1 MCQ

A ball is thrown vertically upwards with a velocity of $20 \mathrm{ms}^{-1}$ from the top of a multistorey building. The height of the point from where the ball is thrown is 25 m from the ground. How long will it take before the ball hits the ground? (Take, $g = 10 \mathrm{ms}^{-2}$)

A

5 s

B

2 s

C

3 s

D

4 s

Question 61: Palette 61/116

Objective Physics Vol-1 MCQ

A ball is thrown upwards from the ground with an initial speed $u$. The ball is at a height of 80 m at two times, for the time interval of 6 s. Find the value of $u$. (Take, $g = 10 \mathrm{ms}^{-2}$)

A

$30 \mathrm{ms}^{-1}$

B

$40 \mathrm{ms}^{-1}$

C

$50 \mathrm{ms}^{-1}$

D

$60 \mathrm{ms}^{-1}$

Question 62: Palette 62/116

Objective Physics Vol-1 MCQ

A particle is thrown vertically upwards from the surface of the earth. Let $T_{P}$ be the time taken by the particle to travel from a point P above the earth to its highest point and back to the point P. Similarly, let $T_{Q}$ be the time taken by the particle to travel from another point Q above the earth to its highest point and back to the same point Q. If the distance between the points P and Q is $H$, find the expression for acceleration due to gravity in terms of $T_{P}$, $T_{Q}$ and $H$.

A

$g = \frac{4H}{T_{P}^{2} - T_{Q}^{2}}$

B

$g = \frac{8H}{T_{P}^{2} - T_{Q}^{2}}$

C

$g = \frac{8H}{T_{P}^{2} + T_{Q}^{2}}$

D

$g = \frac{2H}{T_{P}^{2} - T_{Q}^{2}}$

Question 63: Palette 63/116

Objective Physics Vol-1 MCQ

From the top of a building 16 m high, water drops are falling at equal intervals of time such that when the first drop reaches the ground, the fifth drop just starts. Find the distance between the successive drops at that instant.

A

7 m, 5 m, 3 m, 1 m

B

5 m, 4 m, 3 m, 2 m

C

6 m, 4 m, 3 m, 1 m

D

8 m, 5 m, 3 m, 2 m

Question 64: Palette 64/116

Objective Physics Vol-1 MCQ

A ball is dropped from the top of a tower. After 2 s, another ball is thrown vertically downwards with a speed of $40 \mathrm{ms}^{-1}$. After how much time and at what distance below the top of the tower do the balls meet? (Take, $g = 10 \mathrm{ms}^{-2}$)

A

2 s, 20 m

B

3 s, 45 m

C

4 s, 80 m

D

5 s, 125 m

Question 65: Palette 65/116

Objective Physics Vol-1 MCQ

The velocity-time equation of a particle moving in a straight line is given by $v = 10 + 2t + 3t^2$ (in SI units). If the displacement of the particle is 20 m at time $t = 0$, what is the displacement of the particle at time $t = 1$ s and its corresponding acceleration-time equation?

A

Displacement = 32 m, Acceleration $a = 2 + 6t$

B

Displacement = 20 m, Acceleration $a = 2 + 3t$

C

Displacement = 32 m, Acceleration $a = 10 + 2t$

D

Displacement = 12 m, Acceleration $a = 6t$

Question 66: Palette 66/116

Objective Physics Vol-1 MCQ

The velocity of a particle moving in the positive direction of the X-axis varies as $v = \alpha \sqrt{x}$, where $\alpha$ is a positive constant. Assuming that at moment $t = 0$, the particle was located at the point $x = 0$. What is the time dependence of the velocity of the particle and the mean velocity of the particle averaged over the time that the particle takes to cover the first $s$ metres of the path?

A

$v = \alpha^2 t$, Mean velocity = $\alpha \sqrt{s}$

B

$v = \frac{1}{2} \alpha^2 t$, Mean velocity = $\frac{\alpha \sqrt{s}}{2}$

C

$v = \frac{1}{2} \alpha^2 t$, Mean velocity = $\alpha \sqrt{s}$

D

$v = \alpha^2 t$, Mean velocity = $\frac{\alpha \sqrt{s}}{2}$

Question 67: Palette 67/116

Objective Physics Vol-1 MCQ

If a stone is thrown up with a velocity of $9.8 \text{ ms}^{-1}$, then how much time will it take to come back?

A

1 s

B

2 s

C

3 s

D

4 s

Question 68: Palette 68/116

Objective Physics Vol-1 MCQ

If a ball is thrown vertically upwards with speed $u$, the distance covered during the last $t$ second of its ascent is

A

$ut - (gt^2 / 2)$

B

$(u + gt)t$

C

$ut$

D

$gt^2 / 2$

Question 69: Palette 69/116

Objective Physics Vol-1 MCQ

A person throws balls into air after every second. The next ball is thrown when the velocity of the first ball is zero. How high do the balls rise above his hand?

A

2 m

B

5 m

C

8 m

D

10 m

Question 70: Palette 70/116

Objective Physics Vol-1 MCQ

A particle is thrown vertically upwards. Its velocity at half of the height is $10 \text{ ms}^{-1}$. Then, the maximum height attained by it is (Take, $g = 10 \text{ ms}^{-2}$)

A

16 m

B

10 m

C

20 m

D

40 m

Question 71: Palette 71/116

Objective Physics Vol-1 MCQ

When a ball is thrown up vertically with velocity $v_0$, it reaches a maximum height of $h$. If one wishes to triple the maximum height, then the ball should be thrown with velocity,

A

$\sqrt{3}v_0$

B

$3v_0$

C

$9v_0$

D

$3/2v_0$

Question 72: Palette 72/116

Objective Physics Vol-1 MCQ

A stone thrown upward with a speed $u$ from the top of the tower reaches the ground with a speed $3u$. The height of the tower is

A

$3u^2 / g$

B

$4u^2 / g$

C

$6u^2 / g$

D

$9u^2 / g$

Question 73: Palette 73/116

Objective Physics Vol-1 MCQ

A body thrown vertically up from the ground passes the height of 10.2 m twice in an interval of 10 s. What was its initial velocity?

A

$52 \text{ ms}^{-1}$

B

$61 \text{ ms}^{-1}$

C

$45 \text{ ms}^{-1}$

D

$26 \text{ ms}^{-1}$

Question 74: Palette 74/116

Objective Physics Vol-1 MCQ

A body is projected with a velocity $u$. It passes through a certain point above the ground after $t_1$ second. The time interval after which the body passes through the same point during the return journey is

A

$\left(\frac{u}{g} - t_1^2\right)$

B

$2\left(\frac{u}{g} - t_1\right)$

C

$\left(\frac{u}{g} - t_1\right)$

D

$\left(\frac{u^2}{g^2} - t_1\right)$

Question 75: Palette 75/116

Objective Physics Vol-1 MCQ

A body is thrown vertically upwards from the top A of tower. It reaches the ground in $t_1$ second. If it is thrown vertically downwards from A with the same speed, it reaches the ground in $t_2$ second. If it is allowed to fall freely from A, then the time it takes to reach the ground is given by

A

$t = \frac{t_1 + t_2}{2}$

B

$t = \frac{t_1 - t_2}{2}$

C

$t = \sqrt{t_1 t_2}$

D

$t = \sqrt{\frac{t_1}{t_2}}$

Question 76: Palette 76/116

Objective Physics Vol-1 MCQ

A man in a balloon rising vertically with an acceleration of $4.9 \text{ ms}^{-2}$ releases a ball 2 s after the balloon is let go from the ground. The greatest height above the ground reached by the ball is (Take, $g = 9.8 \text{ ms}^{-2}$)

A

14.7 m

B

19.6 m

C

9.8 m

D

24.5 m

Question 77: Palette 77/116

Objective Physics Vol-1 MCQ

A stone falls freely under gravity. The total distance covered by it in the last second of its journey equals the distance covered by it in first 3 s of its motion. The time for which stone remains in air, is

A

5 s

B

12 s

C

15 s

D

8 s

Question 78: Palette 78/116

Objective Physics Vol-1 MCQ

A body falls from a height $h = 200 \text{ m}$. The ratio of distance travelled in each $2 \text{ s}$, during $t = 0$ to $t = 6 \text{ s}$ of the journey is

A

1:4:9

B

1:2:4

C

1:3:5

D

1:2:3

Question 79: Palette 79/116

Objective Physics Vol-1 MCQ

A ball is released from height $h$ and another from $2h$. The ratio of time taken by the two balls to reach the ground is

A

$1:\sqrt{2}$

B

$\sqrt{2}:1$

C

2:1

D

1:2

Question 80: Palette 80/116

Objective Physics Vol-1 MCQ

A particle is dropped under gravity from rest from a height $h$ ($g = 9.8 \text{ ms}^{-2}$) and it travels a distance $9h / 25$ in the last second, the height $h$ is

A

100 m

B

1225 m

C

145 m

D

167.5 m

Question 81: Palette 81/116

Objective Physics Vol-1 MCQ

A body dropped from the top of a tower covers a distance $7x$ in the last second of its journey, where $x$ is the distance covered in first second. How much time does it take to reach the ground?

A

3 s

B

4 s

C

5 s

D

6 s

Question 82: Palette 82/116

Objective Physics Vol-1 MCQ

The displacement (in metre) of a particle moving along X-axis is given by $x = 18t + 5t^{2}$. The average acceleration during the interval $t_{1} = 2s$ and $t_{2} = 4s$ is

A

$13 \text{ ms}^{-2}$

B

$10 \text{ ms}^{-2}$

C

$27 \text{ ms}^{-2}$

D

$37 \text{ ms}^{-2}$

Question 83: Palette 83/116

Objective Physics Vol-1 MCQ

The displacement of a particle moving in a straight line is described by the relation $s = 6 + 12t - 2t^{2}$. Here, s is in metre and t is in second. The distance covered by particle in first 5 s is

A

20 m

B

32 m

C

24 m

D

26 m

Question 84: Palette 84/116

Objective Physics Vol-1 MCQ

The displacement of a particle moving in a straight line depends on time as $x = \alpha t^{3} + \beta t^{2} + \gamma t + \delta$. The ratio of initial acceleration to its initial velocity depends on

A

$\alpha$ and $\gamma$ only

B

$\beta$ and $\gamma$ only

C

$\alpha$ and $\beta$ only

D

$\alpha$ only

Question 85: Palette 85/116

Objective Physics Vol-1 MCQ

The acceleration of a particle is increasing linearly with time t as bt. The particle starts from the origin with an initial velocity $v_{0}$. The distance travelled by the particle in time t will be

A

$v_{0}t + \frac{1}{6} bt^{3}$

B

$v_{0}t + \frac{1}{3} bt^{3}$

C

$v_{0}t + \frac{1}{3} bt^{2}$

D

$v_{0}t + \frac{1}{2} bt^{2}$

Question 86: Palette 86/116

Objective Physics Vol-1 MCQ

The acceleration $a$ (in $\text{ms}^{-2}$), of a particle is given by $a = 3t^2 + 2t + 2$, where $t$ is the time. If the particle starts out with a velocity $v = 2 \text{ ms}^{-1}$ at $t = 0$, then the velocity at the end of 2 s is

A

12 $\text{ms}^{-1}$

B

14 $\text{ms}^{-1}$

C

16 $\text{ms}^{-1}$

D

18 $\text{ms}^{-1}$

Question 87: Palette 87/116

Objective Physics Vol-1 MCQ

A particle is moving such that $s = t^{3} - 6t^{2} + 18t + 9$, where s is in metre and t is in second. The minimum velocity attained by the particle is

A

29 $\text{ms}^{-1}$

B

5 $\text{ms}^{-1}$

C

6 $\text{ms}^{-1}$

D

12 $\text{ms}^{-1}$

Question 88: Palette 88/116

Objective Physics Vol-1 MCQ

In the position-time graph shown in Example 3.36, what is the nature of acceleration in region OA?

A

Zero

B

Negative

C

Positive

D

Cannot be determined

Question 89: Palette 89/116

Objective Physics Vol-1 MCQ

For region AB in the position-time graph of Example 3.36, what is the value of acceleration?

A

Positive constant

B

Negative constant

C

Zero

D

Variable

Question 90: Palette 90/116

Objective Physics Vol-1 MCQ

In region BC of the position-time graph, the acceleration is:

A

Positive

B

Negative

C

Zero

D

Infinite

Question 91: Palette 91/116

Objective Physics Vol-1 MCQ

What can be said about the motion in region CD of the position-time graph?

A

Velocity is constant

B

Velocity is decreasing

C

Velocity is increasing with positive acceleration

D

Velocity is increasing with negative acceleration

Question 92: Palette 92/116

Objective Physics Vol-1 MCQ

For region DE in the position-time graph, which statement is correct?

A

a > 0, v is increasing

B

a < 0, v is decreasing

C

a = 0, v is constant

D

a is variable, v is variable

Question 93: Palette 93/116

Objective Physics Vol-1 MCQ

With the help of the given velocity-time graph, find the (i) displacement in the first three seconds and (ii) acceleration. (Assume the graph is a straight line starting from $v = 30 \text{ m/s}$ at $t = 0$ and reaching $v = 0 \text{ m/s}$ at $t = 3 \text{ s}$).

A

Displacement = $45 \text{ m}$, Acceleration = $-10 \text{ ms}^{-2}$

B

Displacement = $90 \text{ m}$, Acceleration = $10 \text{ ms}^{-2}$

C

Displacement = $45 \text{ m}$, Acceleration = $10 \text{ ms}^{-2}$

D

Displacement = $90 \text{ m}$, Acceleration = $-10 \text{ ms}^{-2}$

Question 94: Palette 94/116

Objective Physics Vol-1 MCQ

A car accelerates from rest at a constant rate $\alpha$ for some time, after which it decelerates at a constant rate $\beta$ to come to rest. If the total time elapsed is $t$ second, evaluate the maximum velocity reached and the total distance travelled.

A

$\frac{\alpha \beta t}{\alpha + \beta}$ and $\frac{\alpha \beta t^2}{2(\alpha + \beta)}$

B

$\frac{\alpha + \beta}{\alpha \beta t}$ and $\frac{\alpha \beta t^2}{2(\alpha + \beta)}$

C

$\frac{\alpha \beta t}{\alpha + \beta}$ and $\frac{(\alpha + \beta) t^2}{2 \alpha \beta}$

D

$\frac{(\alpha + \beta) t}{\alpha \beta}$ and $\frac{\alpha \beta t^2}{\alpha + \beta}$

Question 95: Palette 95/116

Objective Physics Vol-1 MCQ

A particle moves in a straight line such that its velocity-time graph consists of a triangle from $t=0$ to $t=2$ s reaching $10 \mathrm{m/s}$, a rectangle from $t=2$ to $t=4$ s, a trapezium from $t=4$ to $t=6$ s reaching $20 \mathrm{m/s}$, and a triangle from $t=6$ to $t=8$ s coming to rest. If the initial displacement is zero, what is the total displacement of the particle at the end of 8 seconds?

A

$60 \mathrm{m}$

B

$70 \mathrm{m}$

C

$80 \mathrm{m}$

D

$100 \mathrm{m}$

Question 96: Palette 96/116

Objective Physics Vol-1 MCQ

A rocket is fired vertically upwards with a net acceleration of $4 \, \text{ms}^{-2}$ and initial velocity zero. After 5 s, its fuel is finished and it decelerates with $g$. At the highest point, its velocity becomes zero. Then, it accelerates downwards with acceleration $g$ and returns back to the ground. What is the total time taken for the complete journey? (Take, $g = 10 \, \text{ms}^{-2}$)

A

$7 + \sqrt{14} \, \text{s}$

B

$5 + \sqrt{14} \, \text{s}$

C

$10 + \sqrt{14} \, \text{s}$

D

$12 + \sqrt{14} \, \text{s}$

Question 97: Palette 97/116

Objective Physics Vol-1 MCQ

The acceleration-time graph of a particle moving in a straight line is a triangle with a base of 4 s and a height of $4 \, \text{ms}^{-2}$. If the velocity of the particle at time $t = 0$ is $2 \, \text{ms}^{-1}$, what is the velocity of the particle at the end of the fourth second?

A

$6 \, \text{ms}^{-1}$

B

$8 \, \text{ms}^{-1}$

C

$10 \, \text{ms}^{-1}$

D

$12 \, \text{ms}^{-1}$

Question 98: Palette 98/116

Objective Physics Vol-1 MCQ

The acceleration versus time graph of a particle moving along a straight line is given such that $a = +2 \text{ m/s}^2$ from $t = 0$ to $t = 2 \text{ s}$, $a = 0$ from $t = 2$ to $t = 4 \text{ s}$, and $a = -4 \text{ m/s}^2$ from $t = 4$ to $t = 6 \text{ s}$. Assuming the initial velocity at $t = 0$ is $0 \text{ m/s}$, what is the velocity of the particle at the end of $6 \text{ s}$?

A

$0 \text{ m/s}$

B

$-4 \text{ m/s}$

C

$4 \text{ m/s}$

D

$-8 \text{ m/s}$

Question 99: Palette 99/116

Objective Physics Vol-1 MCQ

Which of the following graph represents the uniform motion?

A

B

C

D

None of these

Question 100: Palette 100/116

Objective Physics Vol-1 MCQ

A particle shows distance-time curve as given in this figure. The maximum instantaneous velocity of the particle is around the point

A

A

B

B

C

C

D

D

Question 101: Palette 101/116

Objective Physics Vol-1 MCQ

From the displacement-time graph, find out the velocity of a moving body. (Assume the graph is a straight line making an angle of $30^\circ$ with the displacement axis).

A

$\frac{1}{\sqrt{3}} \mathrm{ms}^{-1}$

B

$3 \mathrm{ms}^{-1}$

C

$\sqrt{3} \mathrm{ms}^{-1}$

D

$\frac{1}{3} \mathrm{ms}^{-1}$

Question 102: Palette 102/116

Objective Physics Vol-1 MCQ

The distance-time graph of a particle at time t makes an angle $45^\circ$ with the time axis. After one second, it makes an angle $60^\circ$ with the time axis. What is the average acceleration of the particle?

A

$\sqrt{3}$

B

$\sqrt{3} + 1$

C

$\sqrt{3} - 1$

D

$1$

Question 103: Palette 103/116

Objective Physics Vol-1 MCQ

The velocity-time graph of a moving object shows its maximum slope occurring in the time interval from $t = 30 \text{ s}$ to $t = 40 \text{ s}$, where the velocity changes from $20 \text{ cm/s}$ to $80 \text{ cm/s}$. What is the maximum acceleration of the object?

A

$1 \text{ cm s}^{-2}$

B

$2 \text{ cm s}^{-2}$

C

$3 \text{ cm s}^{-2}$

D

$6 \text{ cm s}^{-2}$

Question 104: Palette 104/116

Objective Physics Vol-1 MCQ

The variation of velocity of a particle with time moving along a straight line is illustrated in the adjoining figure. The distance travelled by the particle in 4 s is

A

60 m

B

55 m

C

25 m

D

30 m

Question 105: Palette 105/116

Objective Physics Vol-1 MCQ

A lift is going up. The variation in the speed of the lift is as given in the graph, which forms a trapezium with parallel sides of 12 s and 8 s, and a maximum speed of 3.6 m/s. What is the height to which the lift takes the passengers?

A

3.6 m

B

28.8 m

C

36.0 m

D

Cannot be calculated from the above graph

Question 106: Palette 106/116

Objective Physics Vol-1 MCQ

The velocity-time graph of a body moving in a straight line is shown in the figure. The displacement and distance travelled by the body in 6 s are respectively

A

$8 \mathrm{m}, 16 \mathrm{m}$

B

$16 \mathrm{m}, 32 \mathrm{m}$

C

$16 \mathrm{m}, 16 \mathrm{m}$

D

$8 \mathrm{m}, 18 \mathrm{m}$

Question 107: Palette 107/116

Objective Physics Vol-1 MCQ

The $x - t$ equation is given as $x = 2t + 1$. The corresponding $v - t$ graph is

A

a straight line passing through origin

B

a straight line not passing through origin

C

a parabola

D

None of the above

Question 108: Palette 108/116

Objective Physics Vol-1 MCQ

Which of the following graphs correctly represents the velocity-time relationship for a particle released from rest to fall freely under gravity?

A

B

C

D

Question 109: Palette 109/116

Objective Physics Vol-1 MCQ

A particle is projected vertically upwards and returns to the ground in time $T$. Which of the following graphs correctly represents the variation of velocity ($v$) against time ($t$)?

A

B

C

D

Question 110: Palette 110/116

Objective Physics Vol-1 MCQ

The velocity-time graph for a particle is a straight line starting from $15 \text{ m/s}$ at $t = 0$ and reaching $0 \text{ m/s}$ at $t = 3 \text{ s}$. What is the acceleration of the particle?

A

$225 \text{ ms}^{-2}$

B

$5 \text{ ms}^{-2}$

C

$-5 \text{ ms}^{-2}$

D

$-3 \text{ ms}^{-2}$

Question 111: Palette 111/116

Objective Physics Vol-1 MCQ

The v-t plot of a moving object is shown in the figure. The average velocity of the object during the first 10 s is

A

zero

B

$25 \text{ ms}^{-1}$

C

$5 \text{ ms}^{-1}$

D

$2 \text{ ms}^{-1}$

Question 112: Palette 112/116

Objective Physics Vol-1 MCQ

Which of the following graphs cannot possibly represent one dimensional motion of a particle?

A

I and II

B

II and III

C

II and IV

D

All of these

Question 113: Palette 113/116

Objective Physics Vol-1 MCQ

If the velocity $v$ of a particle moving along a straight line decreases linearly with its displacement $s$ from $20 \text{ ms}^{-1}$ to a value approaching zero at $s = 30 \text{ m}$, then what is the acceleration of the particle at $v = 10 \text{ ms}^{-1}$?

A

$\frac{2}{3} \text{ ms}^{-2}$

B

$-\frac{2}{3} \text{ ms}^{-2}$

C

$\frac{20}{3} \text{ ms}^{-2}$

D

$-\frac{20}{3} \text{ ms}^{-2}$

Question 114: Palette 114/116

Objective Physics Vol-1 MCQ

The $v^2$ versus $s$ graph of a particle moving in a straight line is a straight line with a non-zero intercept on the $v^2$ axis. From the graph, some conclusions are drawn. State which amongst the following statement(s) is wrong?

A

The given graph shows a uniformly accelerated motion.

B

Initial velocity of particle is zero.

C

Corresponding s-t graph will be a parabola.

D

None of the above

Question 115: Palette 115/116

Objective Physics Vol-1 MCQ

A graph between the square of the velocity of a particle and the distance s moved by the particle is shown in the figure below. The acceleration of the particle is

A

$-8\mathrm{ms}^{-2}$

B

$-4\mathrm{ms}^{-2}$

C

$-16\mathrm{ms}^{-2}$

D

None of these

Question 116: Palette 116/116

Objective Physics Vol-1 MCQ

A particle starts from rest at t = 0 and undergoes an acceleration a in ms $^{-2}$ with time t in second which is as shown. Which one of the following plot represents velocity v (in ms $^{-1}$ ) versus time t (in s)?

A

B

C

D