Question

A uniform cylinder of mass $M$ and radius $R$ rolls without slipping down a slope of angle $\theta$ to the horizontal. The cylinder is connected to a spring constant $K$ while the other end of the spring is connected to a rigid support at $P$. The cylinder is released when the spring is unstretched. The maximum distance that the cylinder travels is:

• A. $\frac{3}{4}\frac{Mg\sin \theta }{K}$
• B. $\frac{Mg\tan \theta }{K}$
• C. $\frac{2Mg\sin \theta }{K}$
• D. $\frac{4}{3}\frac{Mg\sin \theta }{K}$

Answer 1

The correct option is C $\frac{2Mg\sin \theta }{K}$

Since, there is no loss of energy to friction due to the stated motion of cylinder.

By using the law of Conservation of energy,

$\frac{1}{2}K{x}^2=Mgx\sin \theta$

$x=\frac{2Mg\sin \theta }{K}$

Thus, the maximum distance travelled by cylinder is $\frac{2Mg\sin \theta }{K}$.