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Work, Power & Energy

769 Questions Start Allen Test
All Exams Allen Advance Errorless
JEE (Main) Jan. 2025 Q1 Errorless Critical Thinking MCQ
A force $\vec{F} = 2\hat{i} + b\hat{j} + \hat{k}$ is applied on a particle and it undergoes a displacement $\vec{s} = (\hat{i} - 2\hat{j} - \hat{k})$ . What will be the value of $b$ , if work done on the particle is zero
A.
0
B.
$\frac{1}{2}$
C.
$\frac{1}{3}$
D.
2
JEE (Main) Jan. 2025 Q2 Errorless Critical Thinking MCQ
A body of mass 100 g is moving in circular path of radius 2 m on vertical plane as shown in figure. The velocity of the body at point A is 10 m/s. The ratio of its kinetic energies at point B and C is
A.
$\frac{2 + \sqrt{3}}{3}$
B.
$\frac{2 + \sqrt{2}}{3}$
C.
$\frac{3 + \sqrt{3}}{2}$
D.
$\frac{3 - \sqrt{2}}{2}$
JEE (Main) Jan. 2025 Q3 Errorless Critical Thinking MCQ
A force $F = \alpha + \beta x^{2}$ acts on an object in the x-direction. The work done by the force is 5 J when the object is displaced by 1 m. If the constant $\alpha = 1N$ then $\beta$ will be
A.
$15 N/m^{2}$
B.
$10 N/m^{2}$
C.
$12 N/m^{2}$
D.
$8 N/m^{2}$
JEE (Main) Jan. 2025 Q4 Errorless Critical Thinking MCQ
A bead of mass ā€˜mā€™ slides without friction on the wall of a vertical circular hoop of radius ā€˜Rā€™ as shown in figure. The bead moves under the combined action of gravity and a massless spring (k) attached to the bottom of the hoop. The equilibrium length of the spring is ā€˜Rā€™. If the bead is released from top of the hoop with (negligible) zero initial speed, velocity of bead, when the length of spring becomes ā€˜Rā€™, would be (spring constant is ā€˜kā€™, g is acceleration due to gravity)
A.
$2\sqrt{gR + \frac{kR^2}{m}}$
B.
$\sqrt{2Rg + \frac{4kR^2}{m}}$
C.
$\sqrt{2Rg + \frac{kR^2}{m}}$
D.
$\sqrt{3Rg + \frac{kR^2}{m}}$
JEF (Main) Jan 2025 Q5 Errorless Critical Thinking MCQ
Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R Assertion A: In a central force field, the work done is independent of the path chosen Reason R: Every force encountered in mechanics does not have an associated potential energy. In the light of the above statements, choose the most appropriate answer from the options given below [JEE (Main) Jan. 2025]
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) Jan. 2025 Q6 Errorless Critical Thinking MCQ
As shown below, bob A of a pendulum having massless string of length 'R' is released from 60Ā° to the vertical. It hits another bob B of half the mass that is at rest on a friction less table in the centre. Assuming elastic collision, the magnitude of the velocity of bob A after the collision will be (take g as acceleration due to gravity)
A.
$\frac{1}{3}\sqrt{Rg}$
B.
$\sqrt{Rg}$
C.
$\frac{4}{3}\sqrt{Rg}$
D.
$\frac{2}{3}\sqrt{Rg}$
JEE (Main) Jan. 2025 Q7 Errorless Critical Thinking MCQ
A body of mass ā€˜mā€™ connected to a massless and unstretchable string goes in vertical circle of radius ā€˜Rā€™ under gravity g. The other end of the string is fixed at the centre of circle. If velocity at top of circular path is $n\sqrt{gR}$ , where, $n \geq 1$ , then ratio of kinetic energy of the body at bottom to that at top of the circle is
A.
$\frac{n}{n+4}$
B.
$\frac{n+4}{n}$
C.
$\frac{n^{2}}{n^{2}+4}$
D.
$\frac{n^{2}+4}{n^{2}}$
JEE (Main) Jan. 2025 Q8 Errorless Critical Thinking MCQ
Given below are two statements. One is labelled as Assertion (A) and the other is labelled as Reason (R) Assertion Three identical spheres of same mass undergo one dimensional motion as shown in figure with initial velocities $v_{A}=5m/s$ , $v_{B}=2m/s$ , $v_{C}=4m/s$ . If we wait sufficiently long for elastic collision to happen, then $v_{A}=4m/s$ , $v_{B}=2m/s$ , $v_{C}=5m/s$ will be the final velocities. Reason (R) : In an elastic collision between identical masses, two objects exchange their velocities. In the light of the above statements, choose the correct 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) Jan. 2024 Q9 Errorless Critical Thinking MCQ
A simple pendulum of length 1 m has a wooden bob of mass 1 kg. It is struck by a bullet of mass $10^{-2}$ kg moving with a speed of $2 \times 10^{2}$ ms $^{-1}$ . The bullet gets embedded into the bob. The height to which the bob rises before swinging back is (use $g = 10 \, m/s^{2}$ )
A.
0.30 m
B.
0.20 m
C.
0.35 m
D.
0.40 m
JEE (Main) Jan. 2024 Q10 Errorless Critical Thinking MCQ
Two bodies of mass 4 g and 25 g are moving with equal kinetic energies. The ratio of magnitude of their linear momentum is
A.
3:5
B.
5:4
C.
2:5
D.
4:5
JEE (Main) Jan. 2024 Q11 Errorless Critical Thinking MCQ
A body of mass 1000 kg is moving horizontally with a velocity 6 m/s. If 200 kg extra mass is added, the final velocity (in m/s) is
A.
6
B.
2
C.
3
D.
5
JEE (Main) Jan. 2024 Q12 Errorless Critical Thinking MCQ
A ball suspended by a thread swings in a vertical plane so that its magnitude of acceleration in the extreme position and lowest position are equal. The angle ( $\theta$ ) of thread deflection in the extreme position will be
A.
$\tan^{-1}(\sqrt{2})$
B.
$2\tan^{-1}\left(\frac{1}{2}\right)$
C.
$\tan^{-1}\left(\frac{1}{2}\right)$
D.
$2\tan^{-1}\left(\frac{1}{\sqrt{5}}\right)$
JEE (Main) Jan. 2024 Q13 Errorless Critical Thinking MCQ
A bob of mass ā€˜mā€™ is suspended by a light string of length ā€˜Lā€™. It is imparted a minimum horizontal velocity at the lowest point A such that it just completes half circle reaching the top most position B. The ratio of kinetic energies $\frac{(K.E.)_{A}}{(K.E.)_{B}}$ is
A.
3:2
B.
5:1
C.
2:5
D.
1:5
JEE (Main) Jan. 2024 Q14 Errorless Critical Thinking MCQ
The potential energy function (in J) of a particle in a region of space is given as $U = (2x^{2} + 3y^{3} + 2z)$ . Here x, y and z are in meter. The magnitude of x-component of force (in N) acting on the particle at point $P(1,2,3)m$ is
A.
2
B.
6
C.
4
D.
8
JEE (Main) Jan. 2024 Q15 Errorless Critical Thinking MCQ
A particle is placed at the point $A$ of a frictionless track $ABC$ as shown in figure. It is gently pushed toward right. The speed of the particle when it reaches the point $B$ is (Take $g = 10m / s^2$ )
A.
$20m / s$
B.
$\sqrt{10} m / s$
C.
$2\sqrt{10} m / s$
D.
$10m / s$
JEE (Main) Jan. 2024 Q16 Errorless Critical Thinking MCQ
An artillery piece of mass $M_{1}$ fires a shell of mass $M_{2}$ horizontally. Instantaneously after the firing, the ratio of kinetic energy of the artillery and that of the shell is
A.
$M_{1}/(M_{1}+M_{2})$
B.
$\frac{M_{2}}{M_{1}}$
C.
$M_{2}/(M_{1}+M_{2})$
D.
$\frac{M_{1}}{M_{2}}$
JEE (Main) Jan. 2024 Q17 Errorless Critical Thinking MCQ
A body of mass 2 kg begins to move under the action of a time dependent force given by $\vec{F} = (6t\hat{i} + 6t^{2}\hat{j})N$ . The power developed by the force at the time t is given by
A.
$(6t^{4} + 9t^{5})W$
B.
$(3t^{3} + 6t^{5})W$
C.
$(9t^{5} + 6t^{3})W$
D.
$(9t^{3} + 6t^{5})W$
JEE (Main) April 2024 Q18 Errorless Critical Thinking MCQ
If a rubber ball falls from a height h and rebounds up to the height of h/2. The percentage loss of total energy of the initial system as well as velocity ball before it strikes the ground, respectively, are
A.
$50\%, \sqrt{\frac{gh}{2}}$
B.
$50\%, \sqrt{gh}$
C.
$40\%, \sqrt{2gh}$
D.
$50\%, \sqrt{2gh}$
JEE (Main) April 2024 Q19 Errorless Critical Thinking MCQ
A particle of mass m moves on a straight line with its velocity increasing with distance according to the equation $v = \alpha \sqrt{x}$ , where $\alpha$ is a constant. The total work done by all the forces applied on the particle during its displacement from x = 0 to x = d, will be
A.
$\frac{m}{2\alpha^{2}d}$
B.
$\frac{md}{2\alpha^{2}}$
C.
$\frac{m\alpha^{2}d}{2}$
D.
$2m\alpha^{2}d$
JEE (Main) April 2024 Q20 Errorless Critical Thinking MCQ
A stationary particle breaks into two parts of masses $m_{A}$ and $m_{B}$ which move with velocities $v_{A}$ and $v_{B}$ respectively. The ratio of their kinetic energies ( $K_{B}:K_{A}$ ) is
A.
$v_{B}:v_{A}$
B.
$m_{B}:m_{A}$
C.
$m_{B}v_{B}:m_{A}v_{A}$
D.
1:1
JEE (Main) April 2024 Q21 Errorless Critical Thinking MCQ
Three bodies A, B and C have equal kinetic energies and their masses are 400 g, 1.2 kg and 1.6 kg respectively. The ratio of their linear momenta is
A.
$1:\sqrt{3}:2$
B.
$1:\sqrt{3}:\sqrt{2}$
C.
$\sqrt{2}:\sqrt{3}:1$
D.
$\sqrt{3}:\sqrt{2}:1$
JEE (Main) April 2024 Q22 Errorless Critical Thinking MCQ
The energy equivalent of 1 g of substance is
A.
$11.2 \times 10^{24}$ MeV
B.
$5.6 \times 10^{12}$ MeV
C.
5.6 eV
D.
$5.6 \times 10^{26}$ MeV
JEE (Main) April 2024 Q23 Errorless Critical Thinking MCQ
A body of $m$ kg slides from rest along the curve of vertical circle from point $A$ to $B$ in friction less path. The velocity of the body at $B$ is (given, R = 14 m, $g = 10m/s^{2}$ and $\sqrt{2} = 1.4$ )
A.
19.8 m/s
B.
21.9 m/s
C.
16.7 m/s
D.
10.6 m/s
JEE (Main) April 2024 Q24 Errorless Critical Thinking MCQ
Four particles A, B, C, D of mass $\frac{m}{2}$ , m, 2m, 4m, have same momentum, respectively. The particle with maximum kinetic energy is
A.
D
B.
C
C.
A
D.
B
JEE (Main) April 2024 Q25 Errorless Critical Thinking MCQ
A body of mass 50 kg is lifted to a height of 20 m from the ground in the two different ways as shown in the figures. The ratio of work done against the gravity in both the respective cases, will be Case-1 : Pulled straight up Case-2 : Along the ramp
A.
1:1
B.
2:1
C.
$\sqrt{3}:2$
D.
1:2