Question

A solid sphere of mass 2 kg is rolling on a frictionless horizontal surface with velocity 6m/s. It collides on the free end 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

• `sqrt14"m"`

• `sqrt2.8"m"`

• `sqrt1.4"m"`

• `sqrt0.7"m"`

Answer 1

A solid sphere of mass 2 kg is rolling on a frictionless horizontal surface with velocity 6m/s. It collides on the free end of an ideal spring whose other end is fixed. The maximum compression produced in the spring will be `underlinebb(sqrt2.8"m")`.

(Force constant of the spring = 36 N/m)

Explanation:

Given, mass, m = 2 kg, v = 6 m/s and force constant K = 36 N/m Kinetic energy of rolling solid sphere

= `1/2"mv"^2+1/2"I"omega^2`

= `12"mv"^2+1/2xx2/5"mr"^2omega^2`

= `1/2"mv"^2+1/5"mv"^2`

= `7/10"mv"^2`

The potential energy of the spring on maximum compression  x = `1/2` kx²

∴ `1/2` kx² = `1/7` mv²

⇒ x² = `14/10"mv"^2/"k"`

= `14/10xx(2xx(6)^2)/36`

= 2.8 

or, x = `sqrt2.8`m