A body of mass m starts moving from rest along x-axis so that its velocity varies as $$\upsilon = a\sqrt s $$ where a is a constant and s is the distance covered by the body. The total work done by all the forces acting on the body in the first t seconds after the start of the motion is :

The relative uncertainly in the period of a satellite orbiting around the earth is 10^-2. If the relative uncertainty in the radius of the orbit is negligible, the relative uncertainty in the mass of the earth is :

Suppose that the angular velocity of rotation of earth is increased. Then, as a consequence :

An oscillator of mass M is at rest in its equilibrium position in a potential
V = $${1 \over 2}$$ k(x $$-$$ X)². A particle of mass m comes from right with speed u and collides completely inelastically with M and sticks to it. This process repeats every time the oscillator crosses its equilibrium position. The amplitude of oscillations after 13 collisions is : (M = 10, m = 5, u = 1, k = 1)