A solid sphere is rolling on a frictionless surface, show in figure with a translational velocity v m/s. If it is to climb the inclined surface then v should be

• ≥ $\sqrt{\raisebox{1ex}{$10$}\!\left/ \!\raisebox{-1ex}{$7\mathrm{gh}$}\right.}$

• ≥ $\sqrt{2\mathrm{gh}}$

• 2gh

• 10/7 gh

A horizontal platform is rotating with uniform angular velocity around the vertical axis passing through its centre. At some instant of time a viscous fluid of mass 'm' is dropped at the centre and is allowed to spread out and finally fall. The angular velocity during this period

• decreases continuously

• decreases initially and increases again

• remains unaltered

• increases continuously

93.

A bomb of mass 3.0 kg in air into two pieces of masses 2.0 kg and 1.0 kg. The smaller mass goes at speed of 80 m/s. The total energy imparted to the two fragments is

• 1.07 kJ

• 2.14 kJ

• 2.4 kJ

• 4.8 kJ

The kinetic energy of a body becomes four times its initial value. The new linear momentum will be

• same as the initial value

• four times the initial value

• twice of the initial value

• eight times of the initial value

Maximum energy transfer for an elastic collision will occur if one body is at rest when

• m₁ = m₂

• m₂ = $\frac{1}{2}$m₁

• m₁ >>  m₂

• m₂ >> m₁

Which of the following is path dependent?

• U

• PdV

• P

• V

Two particles are seen to collide and move jointly together after the collision. During such a collision, for the total system.

• both the mechanical energy and the linear momentum are conserved

• linear momentum is conserved but not the mechanical energy

• neither the mechanical energy nor the linear momentum is conserved

• mechanical energy is conserved but not the linear momentum

A body weighed 250 N on the surface assuming the earth to be a sphere of uniform mass density, how much would it weigh halfway down to the centre of the earth?

• 195 N

• 240 N

• 125 N

• 210 N

Assertion:  Centripetal force does no work. 

Reason:  Force and displacement are perpendicular to each other.

• If both assertion and  reason are true and reason is the correct explanation of assertion.

• If both assertion and reason are true but reason is not the correct explanation of assertion.

• If assertion is true but reason is false.

• If assertion is false but reason is true.

A wire suspended vertically from one of its ends is stretched by attaching a weight of 200 N to the lower end. The weight stretches the wire by 1 mm. Then the elastic energy stored in the wire is

• 20 J

• 0.1 J

• 0.2 J

• 10 J