Two springs of force constant 1000 N/m and 2000 N/m are stretched by same, force. The ratio of their respective potential energies is

• 2 : 1

• 1 : 2

• 4 : 1

• 1 : 4

A particle rests on the top of a hemisphere of radius R. Find the smallest horizontal velocity that must be imparted to the particle, if it is to leave the hemisphere without sliding down it.

• $\sqrt{\mathrm{gR}}$

• $\sqrt{2\mathrm{gR}}$

• $\sqrt{3\mathrm{gR}}$

• $\sqrt{5\mathrm{gR}}$

103.

Two bodies A and B have masses M and m respectively, where M > m and they are at a distance d apart. Equal force is applied to them so that they approach each other. The position where they hit each other is

• nearer to B

• nearer to A

• at equal distance from A and B

• Cannot be predicted

A body of mass m is moving towards the east and another body of equal mass is moving towards the north. If after collision both stick together, their speed after collision would be :

• v

• v/2

• $\sqrt{2}\mathrm{v}$

• $\frac{\mathrm{v}}{\sqrt{2}}$

A body of mass 1 kg is moving in a vertical circular path of radius 1 m. The difference between the kinetic energies at its highest and lowest position is :

• 20 J

• 10 J

• $4\sqrt{5} \mathrm{J}$

• 10($\sqrt{5}$ - 1) J

When a man increases his speed by 2 m/s, he finds that his kinetic energy is doubled, the original speed of the man is :

• $2(\sqrt{2} - 1) \mathrm{m}/\mathrm{s}$

• $2(\sqrt{2} + 1) \mathrm{m}/\mathrm{s}$

• 4.5 m/s

• none of these

A ball falling freely from a height of 4.9 m/s hits a horizontal surface. If e = ¾, then the ball will hit the surface second time after:

• 0.5 s

• 1.5 s

• 3.5 s

• 3.4 s

Hailstone at 0°C falls from a height of 1 km on an insulating surface converting the whole of its kinetic energy into heat. What part of it will melt? (g = 10 m/s²)

• 1/33

• 1/8

• $\frac{1}{3} \times {10}^{-4}$

• All of it will melt

Two bodies of masses m and 2 m have equal kinetic energies. The ratio of their linear momenta is :

• 1

• 1/2

• 1/$\sqrt{2}$

• 2

A ball of mass m elastically collides with a wall with velocity 'v', then change in its momentum is equal to :

• 2m

• 2mv

• + 8mv

• Zero