Two spherical bodies of masses M and SM and radii R and 2R respectively are released in free space with initial separation between their centres equal to 12 R. If they attract each other due to gravitational force only, then the distance covered by the smaller body just before collision,

• 1.5 R

• 2.5 R

• 4.5 R

• 7.5 R

A ball of mass 2 kg moving with velocity 3 m/s collides with spring of natural length 2 m and force constant 144 N/m. What will be length of compressed spring?

• 2 m

• 1.5 m

• 1 m

• 0.5 m

The work done by a force acting on a body is as shown in the graph. The total work done in covering an initial distance of 20 m is

• 225 J

• 200 J

• 400 J

• 175 J

A body of mass m₁ = 4 kg moves at 5 i  m/s and another body of mass m₂ = 2 kg moves at 10 i  m/s. The kinetic energy of centre of mass is

• $\frac{200}{3}\mathrm{J}$

• $\frac{500}{3} \mathrm{J}$

• $\frac{400}{3}\mathrm{J}$

• $\frac{800}{3}\mathrm{J}$

The potential energy of a body is given by U = A - Bx² (where x is the displacement ) The magnitude of force acting on the particle is

• constant

• proportional to x

• proportional to x²

• inversely proportional to x

A gas expands 0.25 m³ at constant pressure 10³ N/m², the work done is

• 250 N

• 250 W

• 250 J

• 2.5 erg

A ball is released from certain height which losses 50% of its kinetic energy on striking the ground it will contain a height again

• $\frac{1}{4}\mathrm{th}$ of initial height

• $\frac{1}{2}\mathrm{th}$ of initial height

• $\frac{3}{4}$th of initial height

• None of the above

If we increase kinetic energy of a body 300%, then per cent increase in its momentum is

• 50%

• 300%

• 100%

• 150%

A particle of mass M and charge Q moving with velocity v describes a circular path of radius R when subjected to a uniform transverse magnetic field of induction B. The work done by the field, when the particle completes one full circle, is

• $\left(\frac{\mathrm{M} {\mathrm{v}}^2}{\mathrm{R}}\right) 2\mathrm{\pi R}$

• zero

• $\mathrm{BQ} 2\mathrm{\pi R}$

• $\mathrm{BQv} 2\mathrm{\pi R}$

130.

A particle of mass 100 g is thrown vertically upward with a speed of 5 m/s. The work done by the force of gravity during the time the particle goes up is 

• -0.5 J

• -1.25 J

• 1.25 J

• 0.5 J