A sphere of mass ' m ' is attached to a spring of spring constant ' k ' and is held in…

A sphere of mass 'm' is attached to a spring of spring constant 'k' and is held in unstretched position over an inclined plane as shown in the figure. After letting the sphere go, find the maximum length by which the spring extends, given the sphere only rolls.

  1. 2mgsin⁡θk
  2. k2mgsin⁡θ
  3. 2sin⁡θkmg
  4. 2mgcos⁡θk

Solution

By applying conservation of energy, loss in gravitational P.E = Gain in P.E of spring.

⇒mgxsinθ=12kx2

⇒2mgsinθ=kx

⇒x=2mgsinθk

Asked in: AP EAMCET 2021 (19 Aug Shift 2)

Practice more Laws of Motion questions on Aicharya