A body of mass 2 kg makes an elastic collision with another body at rest and continues to move in the original direction with one-fourth its original speed. The mass of the second body which collides with the first body is

• 2 kg

• 1.2 kg

• 3 kg

• 1.5 kg

In the stable equilibrium position, a body has 

• maximum potential energy

• minimum potential energy

• minimum kinetic energy

• neither maximum nor minimum potential energy

3.

A particle of mass m at rest is acted upon by a force P for a time t. Its kinetic energy after an interval t is

• $\frac{{\mathrm{P}}^2{\mathrm{t}}^2}{\mathrm{m}}$

• $\frac{{\mathrm{P}}^2{\mathrm{t}}^2}{2\mathrm{m}}$

• $\frac{{\mathrm{P}}^2{\mathrm{t}}^2}{3\mathrm{m}}$

• $\frac{\mathrm{Pt}}{2\mathrm{m}}$

A car of mass 1000 kg accelerates uniformly from rest to a velocity of 54 km/h in 5 s. The average power of the engine during this period in watts is (neglect friction)

• 2000 W

• 22500 W

• 5000 W

• 2250 W

A quarter horse power motor runs at a speed of 600 rpm. Assuming 40% efficiency the work done by the motor in one rotation will be

• 7.46 J

• 7400 J

• 7.46 erg

• 74.6 J

In the HCl molecule, the separation between the nuclei of the two atoms is about 1.27 $\stackrel{\circ }{\mathrm{A}}$ $\left(1 \stackrel{\circ }{\mathrm{A}} = {10}^{-10} \mathrm{m}\right)$. The approximate location of the centre of mass of the molecule, assuming the chlorine atom to be about 35.5 times as massive as hydrogen is

• $1 \stackrel{\circ }{\mathrm{A}}$

• $2.5 \stackrel{\circ }{\mathrm{A}}$

• $1.24 \stackrel{\circ }{\mathrm{A}}$

• $1.5 \stackrel{\circ }{\mathrm{A}}$

A sphere of mass 10 kg and radius 0.5 m rotates about a tangent. The moment of inertia of the sphere is

• 5 kg-m²

• 2.7 kg-m²

• 3.5 kg-m²

• 4.5 kg-m²

A solid sphere (mass 2 m) and a thin spherical shell (mass M) both of the same size, roll down an inclined plane, then

• solid sphere will reach the bottom first

• hollow spherical shell will reach the bottom first

• both will reach at the same time

• cannot be predicted as the data is insufficient

If the earth were to suddenly contract to half the present radius (without any external torque acting on it), by how much would the day be decreased ? (Assume earth to be a perfect solid sphere of moment of inertia $\frac{2}{5} {\mathrm{MR}}^2$)

• 8 h

• 6 h

• 4 h

• 2 h

A research satellite of mass 200 kg circles the earth in an orbit of average radius 3R/2, where R is the radius of the earth. Assuming the gravitational pull on a mass of 1 kg on the earth's surface to be 10 N, the pull on the satellite will be

• 880 N

• 889 N

• 890 N

• 892 N