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Kinematics-2D

362 Questions Start Errorless Test
All Exams Allen Advance Errorless
CPMT 1994 Basic Level Q26 Errorless Centripetal and Centrifugal Force MCQ
A body of mass 4 kg is being rotated with 120 rev. per minute in a horizontal circular path of radius 2m. Its kinetic energy is
A.
2 J
B.
32 J
C.
80 J
D.
1263 J
SCRA 1994 Basic Level Q27 Errorless Bending of Cyclist MCQ
Consider the following statements Assertion (A) : A cyclist always bends inwards while negotiating a curve Reason (R) : By bending he lowers his centre of gravity Of these statements :
A.
If both assertion and reason are true and the reason is the correct explanation of the assertion.
B.
If both assertion and reason are true but reason is not the correct explanation of the assertion.
C.
If assertion is true but reason is false.
D.
If the assertion and reason both are false.
E.
If assertion is false but reason is true.
IIT-JEE 1992 Advance Level Q28 Errorless Centripetal and Centrifugal Force MCQ
A tube of length L is filled completely with an incompressible liquid of mass M and closed at both the ends. The tube is then rotated in a horizontal plane about one of its ends with a uniform angular velocity $\omega$ . The force exerted by the liquid at the other end is
A.
$\frac{ML\omega^{2}}{2}$
B.
$ML\omega^{2}$
C.
$\frac{ML\omega^{2}}{4}$
D.
$\frac{ML^{2}\omega^{2}}{2}$
IIT 1977 Advance Level Q29 Errorless Skidding of Vehicle on Level Road MCQ
The driver of a car travelling at velocity v suddenly see a broad wall in front of him at a distance d. He should
A.
Brake sharply
B.
Turn sharply
C.
(a) and (b) both
D.
None of the above
1920 Q30 Advance SINGLE CORRECT CHOICE TYPE QUESTIONS MCQ
A jet plane flying at a constant velocity $v$ at a height $h = 8$ kilometre is being tracked by a radar $R$ located at $O$ directly below the line of flight. If the angle $\theta$ is decreasing at the rate of $0.025 \, \mathrm{rads}^{-1}$ , the velocity of the plane when $\theta = 60^{\circ}$ is
A.
$1440\mathrm{kmh}^{-1}$
B.
$960\mathrm{kmh}^{-1}$
C.
$1920\mathrm{kmh}^{-1}$
D.
$480\mathrm{kmh}^{-1}$
Basic Level Q31 Errorless Trajectory MCQ
At the top of the trajectory of a projectile, the directions of its velocity and acceleration are
A.
Perpendicular to each other
B.
Parallel to each other
C.
Inclined to each other at an angle of $45^{\circ}$
D.
Antiparallel to each other
Basic Level Q32 Errorless Trajectory MCQ
A stone is projected with an initial velocity at an angle to the horizontal. A small piece separates from the stone before the stone reaches its maximum height. Then this piece will
A.
Fall to the ground vertically
B.
Fly side by side with the parent stone along a parabolic path
C.
Fly horizontally initially and will trace a different parabolic path
D.
Lag behind the parent stone increasing the distance from it
Basic Level Q33 Errorless Trajectory MCQ
A particle moves in the $X - Y$ plane according to the law $x = kt$ and $y = kt(1 - \alpha t)$ , where $k$ and $\alpha$ are positive constants and $t$ is time. What is the equation of trajectory of the particle
A.
$y = kx$
B.
$y = x - \frac{\alpha x^2}{k}$
C.
$y = \frac{\alpha x^2}{k}$
D.
$y = \alpha x$
Basic Level Q34 Errorless Trajectory MCQ
The equation of motion of a projectile is $y = 12x - \frac{3}{4}x^{2}$ . Given that $g = 10 ms^{-2}$ , what is the range of the projectile
A.
12.4 m
B.
16 m
C.
30.6 m
D.
36.0 m
Advance Level Q35 Errorless Trajectory MCQ
A particle is moving in a plane with velocity given by $\vec{u} = u_0\hat{i} + (a\omega \cos \alpha t)\hat{j}$ where $\hat{i},\hat{j}$ are unit vectors along $x$ and $y$ axes respectively. The trajectory of the particle if the particle starts from origin at $t = 0$ will be
A.
$y = a\sin \left(\frac{\omega x}{u_0}\right)$
B.
$y = a\cos \left(\frac{\omega x}{u_0}\right)$
C.
$y = \tan x$
D.
$y = \cos tx$
Advance Level Q36 Errorless Trajectory MCQ
A ball is dropped from the top of a tower in a high speed wind. The wind exerts a steady force on the ball. The path followed by the ball will be
A.
Parabola
B.
Circular arc
C.
Elliptical arc
D.
Straight line
Basic Level Q37 Errorless Velocity MCQ
In a projectile motion, the velocity
A.
Is always perpendicular to the acceleration
B.
Is never perpendicular to the acceleration
C.
Is perpendicular to the acceleration for one instant only
D.
Is perpendicular to the acceleration for two instants
Basic Level Q38 Errorless Velocity MCQ
A body of mass m is thrown upwards at an angle $\theta$ with the horizontal with velocity v. While rising up the velocity of the mass after t seconds will be
A.
$\sqrt{(v\cos\theta)^{2}+(v\sin\theta)^{2}}$
B.
$\sqrt{(v\cos\theta-v\sin\theta)^{2}-gt}$
C.
$\sqrt{v^{2}+g^{2}t^{2}-(2v\sin\theta)gt}$
D.
$\sqrt{v^{2}+g^{2}t^{2}-(2v\cos\theta)gt}$
Basic Level Q39 Errorless Velocity MCQ
A boy throws a ball with a velocity $V_{0}$ at an angle $\alpha$ to the horizontal. At the same instant he starts running with uniform velocity to catch the ball before it hits the ground. To achieve this, he should run with a velocity of
A.
$V_{0} \cos \alpha$
B.
$V_{0} \sin \alpha$
C.
$V_{0} \tan \alpha$
D.
$\sqrt{V_{0}^{2} \tan \alpha}$
Basic Level Q40 Errorless Velocity MCQ
From the top of a tower 19.6 m high, a ball is thrown horizontally. If the line joining the point of projection to the point where it hits the ground makes an angle of $45^{\circ}$ with the horizontal, then the initial velocity of the ball is
A.
$9.8 \, ms^{-1}$
B.
$4.9 \, ms^{-1}$
C.
$14.7 \, ms^{-1}$
D.
$2.8 \, ms^{-1}$
Basic Level Q41 Errorless Velocity MCQ
When a particle is thrown horizontally, the resultant velocity of the projectile at any time $t$ is given by
A.
$gt$
B.
$\frac{1}{2} gt^2$
C.
$\sqrt{u^2 + g^2t^2}$
D.
$\sqrt{u^2 - g^2t^2}$
Basic Level Q42 Errorless Velocity MCQ
A body is thrown horizontally from the top of a tower of height 5 m. It touches the ground at a distance of 10 m from the foot of the tower. The initial velocity of the body is $(g = 10 \, ms^{-2})$
A.
$2.5 \, ms^{-1}$
B.
$5 \, ms^{-1}$
C.
$10 \, ms^{-1}$
D.
$20 \, ms^{-1}$
Basic Level Q43 Errorless Velocity MCQ
An aeroplane is moving with a horizontal velocity u at a height h above the ground. If a packet is dropped from it the speed of the packet when it reaches the ground will be
A.
$(u^{2} + 2gh)^{1/2}$
B.
$(2gh)^{1/2}$
C.
$(u^{2} - 2gh)^{1/2}$
D.
2gh
Advance Level Q44 Errorless Velocity MCQ
A particle is projected with a speed V from a point O making an angle of $30^{\circ}$ with the vertical. At the same instant, a second particle is thrown vertically upwards from a point A. The two particles reach H, the highest point on the parabolic path of particle simultaneously. Then ratio $\frac{V}{v}$ is
A.
$3\sqrt{2}$
B.
$2\sqrt{3}$
C.
$\frac{2}{\sqrt{3}}$
D.
$\frac{\sqrt{3}}{2}$
Advance Level Q45 Errorless Velocity MCQ
Two paper screens (A) and (B) are separated by a distance of 100 m. A bullet pierces (A) and (B) the hole in (B) is 10 cm below the hole is (A). If the bullet is travelling horizontally at the time of hitting (A). Then velocity of the bullet at (A) is
A.
100 m/sec
B.
200 m/sec
C.
600 m/sec
D.
700 m/sec
Advance Level Q46 Errorless Velocity MCQ
A particle is thrown upward with a speed u at an angle $\theta$ with the horizontal. When the particle makes an angle $\phi$ with the horizontal, its speed changes to v, then
A.
$v = u \cos \theta \cos \phi$
B.
$v = u \cos \theta \sec \phi$
C.
$v = u \cos \theta$
D.
$v = u \sec \theta \cos \phi$
Advance Level Q47 Errorless Velocity MCQ
Mr. Naveen kicked off a football with an initial speed 19.6 m/s at a projection angle $45^{\circ}$ . A receiver on the goal line 67.4 m away in the direction of the kick starts running to meet the ball at that instant. What must be his speed so that he could catch the ball before hitting the ground
A.
2.82 m/s
B.
$2/\sqrt{2}$ m/s
C.
39.2 m/s
D.
10 m/s
Advance Level Q48 Errorless Velocity MCQ
Two balls of same mass are thrown horizontally from the top of a tower in the opposite direction with velocities 3 m/s and 4 m/s. The distance between the balls, when their velocities are mutually perpendicular will be nearest to
A.
10 m
B.
7 m
C.
5 m
D.
2.5 m
Advance Level Q49 Errorless Velocity MCQ
A motorcyclist starts from the bottom of a slope of angle $45^{\circ}$ to cross the valley PR as shown in the figure. The width of the valley is 90 m and length of the slope is $80\sqrt{2}m$ . The minimum velocity at point O required to clear the valley will be
A.
70 m/s
B.
30 m/s
C.
50 m/s
D.
100 m/s
Advance Level Q50 Errorless Velocity MCQ
From the top of a tower of height h a body of a mass m is projected in the horizontal direction with a velocity v. It falls on the ground at a distance x from the tower. If a body of mass 2 m is projected from the top of another tower of height 2 h in the horizontal direction so that it falls on the ground at a distance 2x from the tower, the horizontal velocity of the second body is
A.
2 v
B.
$\sqrt{2v}$
C.
$\frac{v}{2}$
D.
$\frac{v}{\sqrt{2}}$