A ball is thrown vertically downwards from a height of 20 m with an initial velocity v0. It collides with the ground, loses 50% of its energy in a collision, and rebounds to the same height. The initial velocity vis:
[Take, g = 10 ms-1]

1. 14 ms-1

2. 20 ms-1

3. 28 ms-1

4. 10 ms-1

Subtopic:  Work Energy Theorem |
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Two similar springs P and Q have spring constants kP and kQ, such that kP> kQ. They are stretched, first by the same amount (case a), then by the same force (case b). The work done by the springs Wand WQ are related as, in case (a) and case (b), respectively :
1. $$W_P=W_Q;W_P>W_Q$$
2. $$W_P=W_Q;W_P=W_Q$$
3. $$W_P>W_Q;W_P<W_Q$$
4. $$W_P<W_Q;W_P<W_Q$$

Subtopic:  Work Energy Theorem |
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A block of mass 10 kg, moving in the x-direction with a constant speed of 10 ms-1 is subjected to a retarding force F = 0.1x J/m during its travel from x = 20 m to 30 m. Its final K.E. will be:

1. 475 J
2. 450 J
3. 275 J
4. 250 J
Subtopic:  Work Energy Theorem |
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A particle of mass m is driven by a machine that delivers a constant power of k watts. If the particle starts from rest, the force on the particle at time t is:

1. $\sqrt{\frac{mk}{2}}{t}^{-1}{2}}$

2. $\sqrt{mk}{t}^{-1}{2}}$

3. $\sqrt{2mk}{t}^{-1}{2}}$

4. $\frac{1}{2}$$\sqrt{mk}{t}^{-1}{2}}$

Subtopic:  Power |
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Two particles of masses m1 and m2 move with initial velocities u1 and u2 respectively. On collision, one of the particles gets excited to a higher level, after absorbing energy E. If the final velocities of particles are v1 and v2, then we must have:

1. ${\mathrm{m}}_{1}^{2}{\mathrm{u}}_{1}+{\mathrm{m}}_{2}^{2}{\mathrm{u}}_{2}-\mathrm{E}={\mathrm{m}}_{1}^{2}{\mathrm{v}}_{1}+{\mathrm{m}}_{2}^{2}{\mathrm{v}}_{2}$

2. $\frac{1}{2}{\mathrm{m}}_{1}{\mathrm{u}}_{1}^{2}+\frac{1}{2}{\mathrm{m}}_{2}{\mathrm{u}}_{2}^{2}=\frac{1}{2}{\mathrm{m}}_{1}{\mathrm{v}}_{1}^{2}+\frac{1}{2}{\mathrm{m}}_{2}{\mathrm{v}}_{2}^{2}$

3. $\frac{1}{2}{\mathrm{m}}_{1}{\mathrm{u}}_{1}^{2}+\frac{1}{2}{\mathrm{m}}_{2}{\mathrm{u}}_{2}^{2}-\mathrm{E}=\frac{1}{2}{\mathrm{m}}_{1}{\mathrm{v}}_{1}^{2}+\frac{1}{2}{\mathrm{m}}_{2}{\mathrm{v}}_{2}^{2}$

4. $\frac{1}{2}{\mathrm{m}}_{1}^{2}{\mathrm{u}}_{1}^{2}+\frac{1}{2}{\mathrm{m}}_{2}^{2}{\mathrm{u}}_{2}^{2}+\mathrm{E}=\frac{1}{2}{\mathrm{m}}_{1}^{2}{\mathrm{v}}_{1}^{2}+\frac{1}{2}{\mathrm{m}}_{2}^{2}{\mathrm{v}}_{2}^{2}$

Subtopic:  Collisions |
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On a frictionless surface, a block of mass M moving at speed v collides elastically with another block of the same mass M which is initially at rest. After the collision, the first block moves at an angle $\theta$ to its initial direction and has a speed $\frac{v}{3}$. The second block’s speed after the collision will be:

1. $\frac{2\sqrt{2}}{3}v$

2. $\frac{3}{4}v$

3. $\frac{3}{\sqrt{2}}v$

4. $\frac{\sqrt{3}}{2}v$

Subtopic:  Collisions |
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A uniform force of $$(3 \hat{i} + \hat{j})$$ newton acts on a particle of mass 2 kg. Hence the particle is displaced from position $$(2 \hat{i} + \hat{k})$$ meter to position $$(4 \hat{i} + 3 \hat{j} - \hat{k})$$ meter. The work done by the force on the particle is:

1. 6 J
2. 13 J
3. 15 J
4. 9 J

Subtopic:  Concept of Work |
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The potential energy of a particle in a force field is U=$\frac{A}{{r}^{2}}-\frac{B}{r}$ where A and B are positive constants and r is the distance of the particle from the center of the field. For stable equilibrium, the distance of the particle is:

1. B/A

2. B/2A

3. 2A/B

4. A/B

Subtopic:  Potential Energy: Relation with Force |
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Two spheres A and B of masses ${\mathrm{m}}_{1}$ and ${\mathrm{m}}_{2}$, respectively, collide. A is at rest initially and B is moving with velocity v along the x-axis. After collision, B has a velocity $\frac{\mathrm{v}}{2}$ in a direction perpendicular to the original direction. The mass A moves after collision in the direction:

1. same as that of B.

2. opposite to that of B.

3.  $\mathrm{\theta }={\mathrm{tan}}^{-1}\left(\frac{1}{2}\right)$ to the positive x-axis.

4. $\mathrm{\theta }={\mathrm{tan}}^{-1}\left(\frac{-1}{2}\right)$ to the positive x-axis

Subtopic:  Collisions |
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A car of mass m starts from rest and accelerates so that the instantaneous power delivered to the car has a
constant magnitude ${P}_{0}$. The instantaneous velocity of this car is proportional to -

1.  ${t}^{1/2}$

2.  ${t}^{-1/2}$

3.  $t/\sqrt{m}$

4.  ${t}^{2}{P}_{0}$

Subtopic:  Power |
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