A sphere of mass $\text{'}m\text{'}$ is attached to a spring of spring constant $\text{'}k\text{'}$ 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.

• Correct answer
  A

  $\frac{2mg\sin \theta }{k}$
• B

  $\frac{k}{2mg\sin \theta }$
• C

  $\frac{2\sin \theta }{kmg}$
• D

  $\frac{2mg\cos \theta }{k}$

Hence, the correct answer is option: 'A'.