In the given figure, a man pulls the mass m with the help of a rope. Work done by the man against gravity when mass is lifted by 0.5 m is: (g = 10 $\mathrm{m}/{\mathrm{s}}^2$)

     
1. 50 J
2. 100 J
3. 25 J
4. Zero

A particle is suspended by a light rod of length l. The minimum speed at which the particle should be projected, so that it moves in a vertical circle, is:

According to the work-energy theorem, the change in kinetic energy of a body is equal to work done by:

1.  Non-conservative force on the particle

2.  Conservative force on the particle

3.  External force on the particle

4.  All the forces on the particle

A block is carried slowly up an inclined plane. If ${\mathrm{W}}_{\mathrm{f}}$ is work done by the friction, ${\mathrm{W}}_{\mathrm{N}}$ is work done by the reaction force, ${\mathrm{W}}_{\mathrm{g}}$ is work done by the gravitational force and ${\mathrm{W}}_{\mathrm{ex}}$ is the work done by an external force, then choose the correct relation(s):

1.  ${\mathrm{W}}_{\mathrm{N}}$ $+$ ${\mathrm{W}}_{\mathrm{f}}$ $+$ ${\mathrm{W}}_{\mathrm{g}}$ $+$ ${\mathrm{W}}_{\mathrm{ex}}$ $=$ $0$

2.  ${\mathrm{W}}_{\mathrm{N}}$ = 0

3.  ${\mathrm{W}}_{\mathrm{ex}}$ $+$ $$ ${\mathrm{W}}_{\mathrm{f}}$ $=$ $-{\mathrm{W}}_{\mathrm{g}}$

4.  All of these

The position of a particle (x) varies with time (t) as \(x = (t - 2)^2\), where x is in meters and t is in seconds. Calculate the work done during t = 0 to t = 4 s if the mass of the particle is 100 g. 
1.  0.4 J
2.  0.2 J
3.  0.8 J
4.  Zero

A particle of mass m is moving in a circular path with a speed v = kt, where k is constant and t is time. The instantaneous power delivered to the particle is: 

A position-dependent force $\mathrm{F}$ $=$ $6$ $+$ $8\mathrm{x}$ $-$ $3{\mathrm{x}}^2$ $\mathrm{N}$ acts on a small body of mass 3 kg, displacing it from x = 0 to x = 2 m. The work done in joule is:

1. 20 J

2.  40 J

3. 10 J

4.  12 J

A car of mass 100 kg and traveling at 20 m/s collides with a truck weighing 1 tonne traveling at 9 km/h in the same direction. The car bounces back at a speed of 5 m/s. The speed of the truck after the impact will be:

1.  11.5 m/s

2.  5 m/s

3.  18 m/s

4.  12 m/s

Which of the following remains unchanged (for the system) during an inelastic collision?

An object of mass m = 1.5 kg is acted upon by the force as shown in the figure that varies with the position of the object as shown. If the object starts from rest at a point x = 0, then what is its speed at x = 50 m?

                    
1. 20 m/s
2. 25 m/s
3. 15 m/s
4. 17 m/s