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1.

A man pushes a wall and fails to displace it. He does:
1. negative work
2. positive but not maximum work
3. no work at all
4. maximum work

2.

A uniform force of \((3 \hat{i} + \hat{j})\) newton acts on a particle of mass \(2~\text{kg}.\) Hence the particle is displaced from the position \((2 \hat{i} + \hat{k})\) metre to the position \((4 \hat{i} + 3 \hat{j} - \hat{k})\) metre. The work done by the force on the particle is:
1. \(6~\text{J}\)
2. \(13~\text{J}\)
3. \(15~\text{J}\)
4. \(9~\text{J}\)

3.

The relationship between force and position is shown in the given figure (in a one-dimensional case). The work done by the force in displacing a body from \(x = 1~\text{cm}\) to \(x = 5~\text{cm}\) is:
      
1.   \(20~\text{ergs}\) 
2.   \(60~\text{ergs}\)
3.   \(70~\text{ergs}\) 
4.   \(700~\text{ergs}\)

4.

The bob of a simple pendulum having length \(l,\) is displaced from the mean position to an angular position \(\theta\) with respect to vertical. If it is released, then the velocity of the bob at the lowest position will be:
1. \(\sqrt{2 g l \left(\right. 1 - \cos \theta \left.\right)}\)
2. \(\sqrt{2 g l \left(\right. 1 + \cos\theta)}\)
3. \(\sqrt{2 g l\cos\theta}\)
4. \(\sqrt{2 g l}\)

5.

A uniform chain of length \(L\) and mass \(M\) is lying on a smooth table and one-third of its length is hanging vertically down over the edge of the table. If \(g\) is the acceleration due to gravity, the work required to pull the hanging part on the table is:
1. \(MgL\)
2. \(\dfrac{MgL}{3}\)
3. \(\dfrac{MgL}{9}\)
4. \(\dfrac{MgL}{18}\)

6.

A mass of \(0.5~\text{kg}\) moving with a speed of \(1.5~\text{m/s}\) on a horizontal smooth surface, collides with a nearly weightless spring with force constant \(k=50~\text{N/m}.\) The maximum compression of the spring would be:
               
1.  \(0.12~\text{m}\) 
2.  \(1.5~\text{m}\) 
3.  \(0.5~\text{m}\) 
4.  \(0.15~\text{m}\) 

7.

The potential energy \(\mathrm{U}\) of a system is given by $\mathrm{U}=$ $\mathrm{A}$ $-$ ${\mathrm{Bx}}^2$ (where \(\mathrm{x}\) is the position of its particle and \(\mathrm{A},\) \(\mathrm{B}\) are constants). The magnitude of the force acting on the particle is:
1. constant
2. proportional to \(\mathrm{x}\)
3. proportional to ${\mathrm{x}}^2$
4. proportional to $\left(\frac{1}{\mathrm{x}}\right)$

8.

When an object is shot from the bottom of a long, smooth inclined plane kept at an angle of \(60^\circ\) $$with horizontal, it can travel a distance \(x_1\) along the plane. But when the inclination is decreased to \(30^\circ\) $$and the same object is shot with the same velocity, it can travel \(x_2\) distance. Then \(x_1:x_2\) will be:

1.	\(1:2\sqrt{3}\)	2.	\(1:\sqrt{2}\)
3.	\(\sqrt{2}:1\)	4.	\(1:\sqrt{3}\)

9. A particle moves with a velocity of \(\left(5\hat{i}-3\hat{j}+6\hat{k}\right)\text{m/s}\) under the influence of a constant force \(\vec F = \left(10\hat{i}+10\hat j +20\hat k\right) \text{N} \). The instantaneous power applied to the particle is:

1.	\(200~\text{J/s}\)	2.	\(40~\text{J/s}\)
3.	\(140~\text{J/s}\)	4.	\(170~\text{J/s}\)

10. Two equal masses, \(m_1\) and \(m_2,\) moving in the same straight line at velocities \(+3~\text{m/s}\) and \(-5~\text{m/s}\) respectively, collide elastically. Their velocities after the collision will be:
1. \(+4~\text{m/s for both}\)
2. \(-3~\text{m/s}~\text{and}+5~\text{m/s}\)
3. \(-4~\text{m/s}~\text{and}+4~\text{m/s}\)
4. \(-5~\text{m/s}~\text{and}+3~\text{m/s}\)