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

• 28 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 linear momentum of S remains constant in magnitude

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

• 3.0

4.

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

• 10.86 kg m²s^-2

• -1

• 2

• zero

• zero

The cylindrical tube of a spray pump has radius R, one end of which has n fine holes, each of radius r. if the speed of the liquid in the tube is v, the speed of the ejection of the liquid through the holes is

• vR²/n²r²

• vR²/nr²

• vR²/n³r²

• vR²/n³r²

Point masses m₁ and m₂ are placed at the opposite ends of a rigid rod of length L and negligible mass. The rod of length L and negligible mass. The rod is to be set rotating about an axis perpendicular to it. The position of point P on this rod through which the axis should pass so that the work required to set the rod rotating with angular velocity ω₀ is minimum is given by 

A plank with a box on it at one end is gradually raised about the other end. As the angle of inclination with the horizontal reaches 30^o, the box starts to slip and slides 4.0 m down the plank in 4.0 s. The coefficients of static and kinetic friction between the box and the plank will be respectively

• 0.6 and 0.6

• 06 and 0.5

• 0.5 and 0.6 

• 0.4 and 0.3

A remote sensing satellite of earth revolves in a circular orbit at a height of 0.25 x 10⁶ m above the surface of the earth. if earth 's radius is 6.38 x 10⁶ m and g = 9.8 ms^-2 then the orbital speed of the  satellite is 

• 7.76 kms^-1

• 8.56 kms^-1

• 9.13 kms^-1

• 9.13 kms^-1

Two stone of masses m and 2m are whirled in horizontal circles, the heavier one in a radius r/2 and the lighter one in radius r. The tangential speed of lighter one in radius r. The tangential speed of lighter stone is n times that of the value of heavier stone when they experience same centripetal forces. The value of n is

• 2

• 3

• 4

• 4