A ball is thrown vertically downwards from a height of 20m with an initial velocity v_o, It collides with the ground, loses 50% of its energy in collision and rebounds to the same height. The initial velocity v_o is,

(Take g = 10 ms^-2)

• 14 ms^-1

• 20 ms^-1

• 28 ms^-1

• 10 ms^-1

A satellite S is moving in an elliptical orbit around the earth. The mass of the satellite is very small as compared to the mass of the earth. Then,

• the angular momentum of S about the centre of the earth changes in direction, but its magnitude remains constant

• the total mechanical energy of S varies periodically with time

• the linear momentum of S remains constant in magnitude

• the acceleration of S is always directed towards the centre of the earth

The heart of a man pumps 5 L of blood through  the arteries per minute at a pressure of 150 mm of mercury . If the density of mercury be 13.6 x 10³ kg/ m³ and g = 10 m/s², then the power of heart in watt is  

• 1.70

• 2.35

• 3.0

• 1.50

An automobile moves on a road with a speed of 54 km h^-1. The radius of its wheels is 0.45 m and the moment of inertia of the wheel about its axis of rotation is 3 kg m² . If the vehicle is brought to rest in 15 s, the magnitude of average torque transmitted by its breaks to the wheel is

• 6.66 kg m²s^-2

• 8.58 kg m²s^-2

• 10.86 kg m²s^-2

• 2.86 kg m²s^-2

 The value of α for which angular momentum about origin is conserved is

• -1

• 2

• zero

• 1