A sphere of mass m and radius R rolls without sliding on a horizontal surface.It collides with a light spring attached to a wall of stiffness k=10N/m with a kinetic enery E=7J.If the surface AB under spring is smooth,prove that maximum compression of spring is 1m.

Spring potential E_s energy is defined as,

E_s = ½ kx²

Here k is the spring constant or stiffness constant and x is the compression or elongation.

In equilibrium, E_K = E_s

=½ kx²

So, compression, x = v[2 E_K/k]

Substitute, 7 J for E_K and 10 N/m for stiffness constant k in the equation x = v[2 E_K/k], we get,

x = v[2 E_K/k]

=v[2(7J)/(10 N/m)]

= 1.18 m

Rounding up to one significant figure, the maximum compression of the spring will be 1 m.