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Q. No.A body of mass \(100~\text g\) is moving in a circular path of radius \(2~\text m\) on a vertical plane as shown in the figure. The velocity of the body at point \(A\) is \(10~\text{m/s}.\) The ratio of its kinetic energies at point \(B\) and \(C\) is: \((\text{use}~g=9.8~\text{m/s}^{2})\)
1.
\(\dfrac{2+\sqrt{2}}{3} \)
2.
\(\dfrac{3+\sqrt{3}}{2} \)
3.
\(\dfrac{2+\sqrt{3}}{3} \)
4.
\(\dfrac{3-\sqrt{2}}{2}\)
Subtopic: Conservation of Mechanical Energy |
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A ball of mass \(100~\text g\) is projected with a velocity of \(20~\text{m/s}\) at an angle of \(60^\circ\) above the horizontal. What is the decrease in its kinetic energy as it moves from the point of projection to the highest point of its trajectory?
1. \(20~\text{J}\)
2. \(5~\text{J}\)
3. zero
4. \(15~\text{J}\)
1. \(20~\text{J}\)
2. \(5~\text{J}\)
3. zero
4. \(15~\text{J}\)
Subtopic: Concept of Work |
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Level 2: 60%+
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As shown below, bob \(A\) of a pendulum having massless string of length \(R\) is released from \(60^{\circ}\) 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 gas acceleration due to gravity)
1. \(\sqrt{{Rg}}\)
2. \(\dfrac{1}{3} \sqrt{{Rg}}\)
3. \(\dfrac{2}{3} \sqrt{2 g}\)
4. \(\dfrac{4}{3} \sqrt{R g}\)
1. \(\sqrt{{Rg}}\)
2. \(\dfrac{1}{3} \sqrt{{Rg}}\)
3. \(\dfrac{2}{3} \sqrt{2 g}\)
4. \(\dfrac{4}{3} \sqrt{R g}\)
Subtopic: Collisions |
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Given below are two statements.
In the light of the above statements, choose the most appropriate answer from the options given below:
| Assertion (A): | Three identical spheres of same mass undergo one dimensional motion as shown in figure with initial velocities \(v_A=5 ~\text{m/s}, v_B=2~\text{m/s}, v_C=4 ~\text{m/s}. ~\) If we wait sufficiently long for elastic collision to happen, then \(v_A=4 ~\text{m/s}, v_B=2~\text{m/s}, v_C=5~\text{m/s}\) 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 most appropriate answer from the options given below:
| 1. | Both (A) and (R) are True and (R) is the correct explanation of (A). |
| 2. | Both (A) and (R) are True but (R) is not the correct explanation of (A). |
| 3. | (A) is True but (R) is False. |
| 4. | (A) is False but (R) is True. |
Subtopic: Collisions |
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A force \(F = \alpha + \beta x^2 \) acts on an object in the \(x-\)direction. The work done by the force is \(5~\text J\) when the object is displaced by \(1~\text m.\) If the constant \(a= 1~\text N\) then \(\beta\) will be:
1. \(12 ~\text {N/m}^2\)
2. \(10 ~\text {N/m}^2\)
3. \(15 ~\text {N/m}^2\)
4. \(8~\text {N/m}^2\)
1. \(12 ~\text {N/m}^2\)
2. \(10 ~\text {N/m}^2\)
3. \(15 ~\text {N/m}^2\)
4. \(8~\text {N/m}^2\)
Subtopic: Work Done by Variable Force |
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Level 1: 80%+
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A sand dropper drops sand of mass \(m(t) \) on a conveyer belt at a rate proportional to the square root of speed \((v)\) of the belt, i.e.
1. \(P \propto \sqrt{v} \)
2. \(P \propto v \)
3. \(P^2 \propto v^5 \)
4. \({P}^2 \propto {v}^3 \)
1. \(P \propto \sqrt{v} \)
2. \(P \propto v \)
3. \(P^2 \propto v^5 \)
4. \({P}^2 \propto {v}^3 \)
Subtopic: Power |
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A force \(F=x^2 y \hat{\imath}+y^2 \hat{\jmath} \) acts on a particle in a plane \(x+y=10.\) The work done by this force during a displacement from \((0,0)\) to \((4~\text m,2~\text m)\) is: (round off to the nearest integer)
1. \(110~\text J\)
2. \(227~\text J\)
3. \(152~\text J\)
4. \(375~\text J\)
1. \(110~\text J\)
2. \(227~\text J\)
3. \(152~\text J\)
4. \(375~\text J\)
Subtopic: Work Done by Variable Force |
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A bead of mass \(m\) slides without friction on the wall of a vertical circular hoop of radius \(R\) 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 \(R.\) If the bead is released from top of the hoop with (negligible) zero initial speed, velocity of bead, when the length of spring becomes \(R,\) would be (spring constant is \(k,\) \(g\) is acceleration due to gravity)
1. \(\sqrt{3 R g+\dfrac{k R^2}{m}}\)
2. \(\sqrt{2 R g+\dfrac{4 k^2}{m}}\)
3. \(2 \sqrt{g R+\dfrac{k R^2}{m}}\)
4. \(\sqrt{2 R g+\dfrac{k R^2}{m}}\)
1. \(\sqrt{3 R g+\dfrac{k R^2}{m}}\)
2. \(\sqrt{2 R g+\dfrac{4 k^2}{m}}\)
3. \(2 \sqrt{g R+\dfrac{k R^2}{m}}\)
4. \(\sqrt{2 R g+\dfrac{k R^2}{m}}\)
Subtopic: Work Energy Theorem |
Level 3: 35%-60%
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A ball having kinetic energy \(KE,\) is projected at an angle of \(60^\circ\) from the horizontal. What will be the kinetic energy of he ball at the highest point of its flight?
1. \(\dfrac{KE}{4}\)
2. \(\dfrac{KE}{16}\)
3. \(\dfrac{KE}{2}\)
4. \(\dfrac{KE}{8}\)
1. \(\dfrac{KE}{4}\)
2. \(\dfrac{KE}{16}\)
3. \(\dfrac{KE}{2}\)
4. \(\dfrac{KE}{8}\)
Subtopic: Concept of Work |
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Level 1: 80%+
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Given below are two statements:
Choose the most appropriate answer from the options given below:
| 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. |
Choose the most appropriate answer from the options given below:
| 1. | Both (A) and (R) are true, but (R) is not the correct explanation of (A) |
| 2. | (A) is false, but (R) is true |
| 3. | Both (A) and (R) are true, and (R) is the correct explanation of (A) |
| 4. | (A) is true, but (R) is false |
Subtopic: Concept of Work |
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