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 10^{3} kg/ m^{3} and g = 10 m/s^{2}, then the power of heart in watt is
1.70
2.35
3.0
3.0
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 m^{2} . 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 m^{2}s^{-2}
8.58 kg m^{2}s^{-2}
10.86 kg m^{2}s^{-2}
10.86 kg m^{2}s^{-2}
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
vR^{2}/n^{2}r^{2}
vR^{2}/nr^{2}
vR^{2}/n^{3}r^{2}
vR^{2}/n^{3}r^{2}
Point masses m_{1} and m_{2} 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 ω_{0} 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 10^{6} m above the surface of the earth. if earth 's radius is 6.38 x 10^{6} 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