Q. No.In a perfectly inelastic collision, two spheres made of the same material with masses \(15~\text{kg}\) and \(25~\text{kg}\), moving in opposite directions with speeds of \(10~\text{m/s}\) and \(30~\text{m/s}\), respectively, strike each other and stick together. The rise in temperature (in \(^{\circ}\text{C}\)), if all the heat produced during the collision is retained by these spheres, is:
(specific heat of sphere material \(31\) cal/kg.oC and \(1\) cal = \(4.2\) J)
1. \(1.75\)
2. \(1.44\)
3. \(1.15\)
4. \(1.95\)
(specific heat of sphere material \(31\) cal/kg.oC and \(1\) cal = \(4.2\) J)
1. \(1.75\)
2. \(1.44\)
3. \(1.15\)
4. \(1.95\)
Subtopic: Collisions |
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Consider two blocks \(A\) and \(B \) of masses \(m_1= 10~\text{kg }\) and \(m_2= 5~\text{kg }\) that are placed on a frictionless table. The block \(A\) moves with a constant speed \(v=3 ~\text{m/s} \) towards the block \(B \) kept at rest. A spring with spring constant \(k=3000 \text{ N/m} ~\) is attached with the block \(B \) as shown in the figure. After the collision, suppose that the blocks \(A \) and \(B, \) along with the spring in constant compression state, move together, then the compression in the spring is: (Neglect the mass of the spring)
1. \(0.1~\text m \)
2. \(0.4~\text m\)
3. \(0.2~\text m\)
4. \(0.3~\text m\)
1. \(0.1~\text m \)
2. \(0.4~\text m\)
3. \(0.2~\text m\)
4. \(0.3~\text m\)
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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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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A stationary particle breaks into two parts of masses \(\mathrm{m_A}\) and \(\mathrm{m_B}\) which move with velocities \(\mathrm{v_A}\) and \(\mathrm{v_B}\) respectively. The ratio of their kinetic energies \(\mathrm{(K_B:K_A)}\) is:
1. \(\mathrm{m_B:m_A}\)
2. \(1:1\)
3. \(\mathrm{m_Bv_B:m_Av_A}\)
4. \(\mathrm{v_B:v_A}\)
1. \(\mathrm{m_B:m_A}\)
2. \(1:1\)
3. \(\mathrm{m_Bv_B:m_Av_A}\)
4. \(\mathrm{v_B:v_A}\)
Subtopic: Collisions |
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A ball dropped from height \(H\) rebounds up to height \(h\) after colliding with a horizontal surface. If the coefficient of restitution for collision is \(e=\dfrac{1}{2}\) then the ratio of \(\dfrac{H}{h}\) is:
1. \(5\)
2. \(4\)
3. \(2\)
4. \(1\)
1. \(5\)
2. \(4\)
3. \(2\)
4. \(1\)
Subtopic: Collisions |
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A rubber ball falls on the floor from height \(h\) and bounces back up to height \(\frac{h}{2}.\) The percentage loss in energy and velocity of the ball just before striking are respectively:
1. \(50 \%, \sqrt{2 g h} \)
2. \(40 \%, \sqrt{2 g h} \)
3. \(50 \%, \sqrt{g h} \)
4. \(40 \%, \sqrt{g h} \)
1. \(50 \%, \sqrt{2 g h} \)
2. \(40 \%, \sqrt{2 g h} \)
3. \(50 \%, \sqrt{g h} \)
4. \(40 \%, \sqrt{g h} \)
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A particle of mass \(m\) moving with velocity \(v\) collides with a stationary particle of mass \(2m\) and sticks to it. The velocity of the combined mass (system) will be:
| 1. | \(v\) | 2. | \(\dfrac{v}{2}\) |
| 3. | \(\dfrac{v}{3}\) | 4. | \(\dfrac{v}{4}\) |
Subtopic: Collisions |
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A ball was dropped from \(20\) m height from the ground. The height up to which it rises after the collision is: (Use \(e={{1}\over{2}} \) , \(g=10\) m/s2 )
1. \(3\) m
2. \(5\) m
3. \(10\) m
4. \(6\) m
1. \(3\) m
2. \(5\) m
3. \(10\) m
4. \(6\) m
Subtopic: Collisions |
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What is the initial speed of a \(10~\text{g}\) bullet that strikes a stationary \(200~\text{g}\) ball at a height of \(20\) m, if after the horizontal collision the bullet travels \(120\) m horizontally and the ball travels \(30\) horizontally before hitting the ground (take \(g=10\) m/s²)?
1. \(150\) m/s
2. \(90\) m/s
3. \(240\) m/s
4. \(360\) m/s
1. \(150\) m/s
2. \(90\) m/s
3. \(240\) m/s
4. \(360\) m/s
Subtopic: Collisions |
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