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Q. No.A bob of mass m is suspended at a point \(O\) by a light string of length l and left to perform vertical motion (circular) as shown in figure. Initially, by applying horizontal velocity \(v_0\) at the point A the string becomes slack when, the bob reaches at the point \(D\). The ratio of the kinetic energy of the bob at the points \(B\) and \(C\) is _____.
1. \(3\)
2. \(1\)
3. \(4\)
4. \(2\)
Subtopic: Conservation of Mechanical Energy |
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A force \(\vec F = 2 \hat i + b \hat j + \hat k\) is applied on a particle and it undergoes a displacement \(\hat i - 2 \hat j - \hat k.\) What will be the value of \(b,\) if work done on the particle is zero
1. \(2\)
2. \(0\)
3. \(\dfrac{1}{3}\)
4. \(\dfrac{1}{2}\)
1. \(2\)
2. \(0\)
3. \(\dfrac{1}{3}\)
4. \(\dfrac{1}{2}\)
Subtopic: Work done by constant force |
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A body of mass \(m\) connected to a massless and unstretchable string goes in vertical circle of radius \(R \) 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, \(n>1 \), then ratio of kinetic energy of the body at bottom to that at top of the circle is:
1. \(\dfrac{n+4}{n}\)
2. \(\dfrac{n^2}{n^2+4}\)
3. \(\dfrac{n}{n+4}\)
4. \(\dfrac{n^2+4}{n^2}\)
1. \(\dfrac{n+4}{n}\)
2. \(\dfrac{n^2}{n^2+4}\)
3. \(\dfrac{n}{n+4}\)
4. \(\dfrac{n^2+4}{n^2}\)
Subtopic: Conservation of Mechanical Energy |
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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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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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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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