The SI unit of gravitational potential is

• J

• J-kg^-1

• J-kg

• J-kg²

The magnitude of a vector, on the addition of two vectors $6\stackrel{\wedge }{\mathrm{i}} + 7\stackrel{\wedge }{\mathrm{j}} \mathrm{and} 3\stackrel{\wedge }{\mathrm{i}} + 4\stackrel{\wedge }{\mathrm{j}}$ is

• $\sqrt{132}$

• $\sqrt{136}$

• $\sqrt{160}$

• $\sqrt{202}$

The potential energy of a particle varies with distance x from a fixed origin as $\mathrm{V} = \left(\frac{\mathrm{A}\sqrt{\mathrm{x}}}{\mathrm{x} + \mathrm{B}}\right)$ ; where A and B are constants. The dimensions of AB are

• $\left[{\mathrm{ML}}^{5/2}{\mathrm{T}}^{-2}\right]$

• $\left[{\mathrm{ML}}^2{\mathrm{T}}^{-2}\right]$

• $\left[{\mathrm{M}}^{3/2}{\mathrm{L}}^{3/2}{\mathrm{T}}^{-2}\right]$

• $\left[{\mathrm{ML}}^{7/2}{\mathrm{T}}^{-2}\right]$

The acceleration experienced by a moving boat after its engine is cut off, is given by a = − kv³, where k is a constant. If v₀ is the magnitude of velocity at cut off, then the magnitude of the velocity at time t after the cut off is

• $\frac{{\mathrm{v}}_0}{2{{\mathrm{ktv}}_0}^2}$

• $\frac{{\mathrm{v}}_0}{1 + 2{{\mathrm{ktv}}_0}^2}$

• $\frac{{\mathrm{v}}_0}{\sqrt{1 - 2{{\mathrm{kv}}_0}^2}}$

• $\frac{{\mathrm{v}}_0}{\sqrt{1 + 2{{\mathrm{ktv}}_0}^2}}$

A passenger train is moving at 5 ms^-1 .An express train is travelling at 30 ms^-1, on the same track and rear side of the passenger train at some distance. The driver in express train applied brakes to avoid collision. If the retardation due to brakes is 4 ms^-2 , the time in which the accident is avoided after the application of brakes is

• 4.25 s

• 5.25 s

• 6.25 s

• 7.25 s

6.

A weightless thread can bear tension upto 37 N. A stone of mass 500 g is tied to it and revolved in a circular path of radius 4 m in a vertical plane. If g = 10 ms^-2, then the maximum angular velocity of the stone will be

• 2 rad s^-1

• 4 rad s^-1

• 8 rad s^-1

• 16 rad s^-1

The pulleys and strings shown in the figure are smooth and of negligible mass. For the system to remain in equilibrium, the angle θ should be

• 0°

• 30°

• 45°

• 60°

A force-time graph for a linear motion of a body is shown in the figure. The change in linear momentum between O and 7 s is

• 2 N-s

• 3 N-s

• 4 N-s

• 5 N-s

Figure shows two blocks A and B pushed against the smooth wall with the force F. The wall is smooth but the surfaces in contact of A and B arerough. Which of the following is true for the system of blocks ?

• The system can not be in equilibrium

• F should be equal to weight of A and B

• F should be less than theweight of A and B

• F should be more than the weight of A and B

A small block is shot into each of the four tracks as shown below. Each of the  frictionless track rises to the same height. The speed, with which the block enters the tracks, is same in all cases. At the highest point of the track; normal reaction is maximum in