The dimensions of  are

• [L^1/2 T^-1/2]

• [L^-1T]

• [LT^-1]

• [LT^-1]

A stone is dropped from a height h. It hits the ground with a certain momentum p. If the same stone is dropped from a height 100% more than the previous height, the momentum when it hits the ground will change by

• 68%

• 41%

• 200%

• 200%

A car of mass m starts from rest and accelerates so that the instantaneous power delivered to the car has a constant magnitude P_o. The instantaneous velocity of this car is proportional to

• t²P_o

• t^1/2

• t^-1/2

• t^-1/2

A car of mass m is moving on a level circular track of radius R. If  represents the static friction between the road and tyres of the car, the maximum speed of the car in circular motion is given by

A circular platform is mounted on the frictionless vertical axle. Its radius R =2 m and its moment of inertia about the axle is 200 kg m². It is initially at rest. A 50 kg man stands on the edge of the platform and begins to walk along the edge at the speed of 1 ms^-1 relative to the ground. Time taken by the man to complete one revolution is

• π sec

• 3π/2 sec

• 2π sec

• 2π sec

The moment of inertia of a uniform circular disc is maximum about an axis perpendicular to the disc and passing through

• B

• C

• D

• D

Three masses are placed on the x- axis: 300g at origin, 500g at x = 40 cm and 400 g at x = 70 cm. The distance of the centre of mass from the origin is 

• 40 cm

• 45 cm

• 50 cm

• 50 cm

If v_e is escape velocity and v_o is orbital velocity of a satellite for orbit close to the Earth's surface, then these are related by

Which one of the following plots represents the variation of the gravitational field on a particle with distance r due to a thin spherical shell of radius R? (r is measured from the centre of the spherical shell).

A slab of stone of area of 0.36 m² and thickness 0.1 m is exposed on the lower surface to steam at 100^oC. A block of ice at 0^o C rests on the upper surface of the slab. In one hour 4.8 kg of ice is melted. The thermal conductivity of slab is
(Given latent heat of fusion of ice = 3.36 x 10⁵ J Kg^-1)

• 1.24 J/m/s/^oC

• 1.29 J/m/s^oC

• 2.05 J/m/s^o C

• 2.05 J/m/s^o C