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Work, Power & Energy

238 Questions Start Errorless Test
All Exams Allen Advance Errorless
JEE (Main) July 2022 Q51 Errorless 7. Critical Thinking MCQ
Sand is being dropped from a stationary dropper at a rate of $0.5 \, kgs^{-1}$ on a conveyor belt moving with a velocity of $5 \, ms^{-1}$ . The power needed to keep belt moving with the same velocity will be
A.
1.25 W
B.
2.5 W
C.
6.25 W
D.
12.5 W
JEE (Main) June 2022 Q52 Errorless 8. Graphical Questions MCQ
Arrange the four graphs in descending order of total work done; where $W_{1}, W_{2}, W_{3}$ and $W_{4}$ are the work done corresponding to figure 1, 2, 3 and 4 respectively Figure-1 $F\uparrow$ Figure-2 $F\uparrow$ Figure-3 $F\uparrow$ Figure-4 $F\uparrow$
A.
$W_{3} > W_{2} > W_{1} > W_{4}$
B.
$W_{3} > W_{2} > W_{4} > W_{1}$
C.
$W_{2} > W_{3} > W_{4} > W_{1}$
D.
$W_{2} > W_{3} > W_{1} > W_{4}$
JEE (Main) July 2022 Q53 Errorless 8. Graphical Questions MCQ
A bullet is shot vertically downwards with an initial velocity of 100 m/s from a certain height. Within 10 s, the bullet reaches the ground and instantaneously comes to rest due to the perfectly inelastic collision. The velocity-time curve for total time t = 20 s will be (Take $g = 10 \, m/s^{2}$ )
A.
a
B.
b
C.
c
D.
d
JEE (Main) Feb. 2021 Q54 Errorless 7. Critical Thinking MCQ
Given below are two statements: one is labelled as assertion A and the other is labelled as reason R Assertion A : Body 'P' having mass M moving with speed 'u' has head-on collision elastically with another body 'Q' having mass 'm' initially at rest. If m << M, body 'Q' will have a maximum speed equal to '2u' after collision. Reason R : During elastic collision, the momentum and kinetic energy are both conserved. In the light of the above statements, choose the most appropriate answer from the options given below
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.
JEE (Main) March 2021 Q55 Errorless 7. Critical Thinking MCQ
An object of mass $m_{1}$ collides with another object of mass $m_{2}$ , which is at rest. After the collision the objects move with equal speeds in opposite direction. The ratio of the masses $m_{2}:m_{1}$ is
A.
3:1
B.
2:1
C.
1:2
D.
1:1
JEE (Main) March 2021 Q56 Errorless 7. Critical Thinking MCQ
A large block of wood of mass $M = 5.99 \, kg$ is hanging from two long massless cords. A bullet of mass $m = 10g$ is fired into the block and gets embedded in it. The (block + bullet) then swing upwards, their centre of mass rising a vertical distance $h = 9.8 \, cm$ before the (block + bullet) pendulum comes momentarily to rest at the end of its arc. The speed of the bullet just before collision is (Take $g = 9.8 \, ms^{-2}$ )
A.
841.4 m/s
B.
811.4 m/s
C.
831.4 m/s
D.
821.4 m/s
JEE (Main) March 2021 Q57 Errorless 7. Critical Thinking MCQ
A boy is rolling a 0.5 kg ball on the frictionless floor with the speed of $20 \, ms^{-1}$ . The ball gets deflected by an obstacle on the way. After deflection it moves with 5% of its initial kinetic energy. What is the speed of the ball now
A.
$19.0 \, ms^{-1}$
B.
$4.47 \, ms^{-1}$
C.
$14.41 \, ms^{-1}$
D.
$1.00 \, ms^{-1}$
JEE (Main) March 2021 Q58 Errorless 7. Critical Thinking MCQ
A constant power delivering machine has towed a box, which was initially at rest, along a horizontal straight line. The distance moved by the box in time 't' is proportional to
A.
$t^{2/3}$
B.
$t^{3/2}$
C.
t
D.
$t^{1/2}$
JEE (Main) July 2021 Q59 Errorless 7. Critical Thinking MCQ
A porter lifts a heavy suitcase of mass 80 kg and at the destination lowers it down by a distance of 80 cm with a constant velocity. Calculate the workdone by the porter in lowering the suitcase (take $g = 9.8 ms^{-2}$ )
A.
-62720.0 J
B.
-627.2 J
C.
+627.2 J
D.
784.0 J
JEE (Main) July 2021 Q60 Errorless 7. Critical Thinking MCQ
Three objects A, B and C are kept in a straight line on a frictionless horizontal surface. The masses of A, B and C are m, 2 m and 2 m respectively. A moves towards B with a speed of 9 m/s and makes an elastic collision with it. Thereafter B makes a completely inelastic collision with C. All motions occur along same straight line. The final speed of C is
A.
6 m/s
B.
9 m/s
C.
4 m/s
D.
3 m/s
JEE (Main) July 2021 Q61 Errorless 7. Critical Thinking MCQ
Given below is the plot of a potential energy function $U(x)$ for a system, in which a particle is in one dimensional motion, while a conservative force $F(x)$ acts on it. Suppose that $E_{mech} = 8J$ , the incorrect statement for this system is [where K.E. = kinetic energy]
A.
At $x > x_{4}$ K.E. is constant throughout the region
B.
At $x < x_{1}$ , K.E. is smallest and the particle is moving at the slowest speed
C.
At $x = x_{2}$ , K.E. is
greatest and the particle is moving at the fastest speed
D.
At $x = x_{3}$ , K.E. $= 4J$
JEE (Main) July 2021 Q62 Errorless 7. Critical Thinking MCQ
An automobile of mass 'm' accelerates starting from origin and initially at rest, while the engine supplies constant power P. The position is given as a function of time by
A.
$\left(\frac{9P}{8m}\right)^{\frac{1}{2}}t^{\frac{3}{2}}$
B.
$\left(\frac{8P}{9m}\right)^{\frac{1}{2}}t^{\frac{2}{3}}$
C.
$\left(\frac{9m}{8P}\right)^{\frac{1}{2}}t^{\frac{3}{2}}$
D.
$\left(\frac{8P}{9m}\right)^{\frac{1}{2}}t^{\frac{3}{2}}$
JEE (Main) Aug. 2021 Q63 Errorless 7. Critical Thinking MCQ
A body of mass 'm' dropped from a height 'h' reaches the ground with a speed of $0.8\sqrt{gh}$ . The value of work done by the air – friction is
A.
-0.68 mgh
B.
0.64 mgh
C.
mgh
D.
1.64 mgh
JEE (Main) Aug. 2021 Q64 Errorless 7. Critical Thinking MCQ
A block moving horizontally on a smooth surface with a speed of 40 m/s splits into two parts with masses in the ratio of 1:2. If the smaller part moves at 60 m/s in the same direction, then the fractional change in kinetic energy is
A.
$\frac{1}{8}$
B.
$\frac{2}{3}$
C.
$\frac{1}{3}$
D.
$\frac{1}{4}$
JEE (Advanced) 2021 Q65 Errorless 9. JEE Section Numerical
A pendulum consists of a bob of mass m = 0.1 kg and a massless inextensible string of length L = 1.0 m. It is suspended from a fixed point at height H = 0.9 m above a frictionless horizontal floor. Initially, the bob of the pendulum is lying on the floor at rest vertically below the point of suspension. A horizontal impulse P = 0.2 kg - m / s is imparted to the bob at some instant. After the bob slides for some distance, the string becomes taut and the bob lifts off the floor. The magnitude of the angular momentum of the pendulum about the point of suspension just before the bob lifts off is J kg·m²/s. The kinetic energy of the pendulum just after the lift-off is K Joules. The value of $J$ is
JEE (Advanced) 2021 Q66 Errorless 9. JEE Section Numerical
A pendulum consists of a bob of mass m = 0.1 kg and a massless inextensible string of length L = 1.0 m. It is suspended from a fixed point at height H = 0.9 m above a frictionless horizontal floor. Initially, the bob of the pendulum is lying on the floor at rest vertically below the point of suspension. A horizontal impulse P = 0.2 kg - m / s is imparted to the bob at some instant. After the bob slides for some distance, the string becomes taut and the bob lifts off the floor. The magnitude of the angular momentum of the pendulum about the point of suspension just before the bob lifts off is J kg·m²/s. The kinetic energy of the pendulum just after the lift-off is K Joules. The value of $K$ is
JEE (Main) Jan. 2020 Q67 Errorless 7. Critical Thinking MCQ
A 60 HP electric motor lifts an elevator having a maximum total load capacity of $2000\mathrm{kg}$ . If the frictional force on the elevator is $4000N$ , the speed of the elevator at full load is close to $(1\mathrm{HP} = 746W, g = 10ms^{-2})$
A.
$1.7ms^{-1}$
B.
$2.0ms^{-1}$
C.
$1.9ms^{-1}$
D.
$1.5ms^{-1}$
JEE (Main) Jan. 2020 Q68 Errorless 7. Critical Thinking MCQ
An elevator in a building can carry a maximum of 10 persons, with the average mass of each person being $68\mathrm{kg}$ . The mass of the elevator itself is $920\mathrm{kg}$ and it moves with a constant speed $3\mathrm{m / s}$ . The frictional force opposing the motion is $6000N$ . If the elevator is moving up with its full capacity, the power delivered by the motor to the elevator $(g = 10m / s^2)$ must be at least
A.
$56300W$
B.
$48000W$
C.
$66000W$
D.
$62360W$
JEE (Main) Jan. 2020 Q69 Errorless 7. Critical Thinking MCQ
A particle of mass m is dropped from a height h above the ground. At the same time another particle of the same mass is thrown vertically upwards from the ground with a speed of $\sqrt{2gh}$ . If they collide head-on completely inelastically, the time taken for the combined mass to reach the ground, in units of $\sqrt{\frac{h}{g}}$ is
A.
$\frac{1}{2}$
B.
$\sqrt{\frac{1}{2}}$
C.
$\sqrt{\frac{3}{4}}$
D.
$\sqrt{\frac{3}{2}}$
JEE (Main) Jan. 2020 Q70 Errorless 7. Critical Thinking MCQ
Two particles of equal mass m have respective initial velocities $u\hat{i}$ and $u\left(\frac{\hat{i}+\hat{j}}{2}\right)$ . They collide completely inelastically. The energy lost in the process is
A.
$3/4mu^{2}$
B.
$1/8mu^{2}$
C.
$\sqrt{\frac{2}{3}}mu^{2}$
D.
$\frac{1}{3}mu^{2}$
JEE (Main) Jan. 2020 Q71 Errorless 7. Critical Thinking MCQ
A particle of mass m is projected with a speed u from the ground at an angle $\theta=\frac{\pi}{3}w.r.t.$ horizontal (x-axis). When it has reached its maximum height, it collides completely inelastically with another particle of the same mass and velocity $u\hat{i}$ . The horizontal distance covered by the combined mass before reaching the ground is
A.
$\frac{3\sqrt{2}}{4}\frac{u^{2}}{g}$
B.
$2\sqrt{2}\frac{u^{2}}{g}$
C.
$\frac{3\sqrt{3}}{8}\frac{u^{2}}{g}$
D.
$\frac{5}{8}\frac{u^{2}}{g}$
JEE (Main) Sep. 2020 Q72 Errorless 7. Critical Thinking MCQ
A particle of mass m with an initial velocity $u\hat{i}$ collides perfectly elastically with a mass 3m at rest. It moves with a velocity $v\hat{j}$ after collision, then v is given by
A.
$v = \sqrt{\frac{2}{3}}u$
B.
$v = \frac{u}{\sqrt{3}}$
C.
$v = \frac{1}{\sqrt{6}}u$
D.
$v = \frac{u}{\sqrt{2}}$
JEE (Main) Sep. 2020 Q73 Errorless 7. Critical Thinking MCQ
A block of mass 1.9 kg is at rest at the edge of a table, of height 1 m. A bullet of mass 0.1 kg collides with the block and sticks to it. If the velocity of the bullet is 20 m/s in the horizontal direction just before the collision then the kinetic energy just before the combined system strikes the floor, is [Take $g = 10m/s^{2}$ . Assume there is no rotational motion and loss of energy after the collision is negligible]
A.
21 J
B.
23 J
C.
20 J
D.
19 J
JEE (Main) Sep. 2020 Q74 Errorless 7. Critical Thinking MCQ
Blocks of masses m, 2m, 4m and 8m are arranged in a line on a frictionless floor. Another block of mass m, moving with speed v along the same line (see figure) collides with mass m in perfectly inelastic manner. All the subsequent collisions are also perfectly inelastic. By the time the last block of mass 8m starts moving the total energy loss is p% of the original energy. Value of ‘p’ is close to image.png
A.
77
B.
37
C.
87
D.
94
JEE (Main) Sep. 2020 Q75 Errorless 7. Critical Thinking MCQ
A person pushes a box on a rough horizontal platform surface. He applies a force of 200 N over a distance of 15m. Thereafter, he gets progressively tired and his applied force reduces linearly with distance to 100 N. The total distance through which the box has been moved is 30 m. What is the work done by the person during the total movement of the box
A.
5250 J
B.
3280 J
C.
2780 J
D.
5690 J