A solid sphere of mass 2 kg is rolling on a frictionless horizontal surface with velocity `6 m//s`. It collides on the free and of an ideal spring whose other end is fixed. The maximum compression produced in the spring will be
(Force constant of the spring = 36 N/m)

Options

A. `sqrt14 m`
B. `sqrt(2.8)m`
C. `sqrt(1.4)m`
D. `sqrt(0.7)m`

Answer

B

Explanation

Kinetic energy of rolling solid sphere,
`KE=1/2mv^(2)[1+k^(2)//R^(2)]`
`=1/2mv^(2)[1+2/5]`
`=1/2mv^(2)xx7/5=(7mv^(2))/(10)`
The potential energy of the spring on maximum compression `x=1/2kx^(2)`
By the law of conservation of energy.
`x=1/2kx^(2)=7/10mV^(2)`
`x^(2)=(14mV^(2))/(10k)`
`=14/10xx(2xx(6)^(2))/(36)=2.8`
`therefore x=sqrt(2.8)m`