Frame of Reference

Q. A uniform cylinder of mass $m$ and radius $R$ rolls without slipping down a slope of angle $\theta$ with the horizontal. The cylinder is connected to a spring having 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 travel along the plane is

1. $\frac{3mg\sin \theta }{4K}$
2. $\frac{mg\sin \theta }{K}$
3. $\frac{2mg\sin \theta }{K}$
4. $\frac{4mg\sin \theta }{3K}$

Q.

A block of mass m rigidly attached with a spring k is compressed through a distance A. If the block is released, the period of oscillation of the block for a complete cycle is equal to

1. 

2. 

3. 

4. $\frac{5\pi }{3}\sqrt{\frac{m}{k}}$

Q. A block is moving with a velocity of $10\text{m/s}$ and the observer is moving in the opposite direction at a speed of $20\text{m/s}$. Find the ratio of the kinetic energy of block w.r.t ground to the kinetic energy of block w.r.t observer.

1. $\frac{1}{3}$
2. $\frac{1}{9}$
3. $\frac{1}{2}$
4. value of mass is necessary to determine the ratio.

Q. A uniform cylinder of mass $m$ and radius $R$ rolls without slipping down a slope of angle $\theta$ with the horizontal. The cylinder is connected to a spring having 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 travel along the plane is

1. $\frac{3mg\sin \theta }{4K}$
2. $\frac{mg\sin \theta }{K}$
3. $\frac{2mg\sin \theta }{K}$
4. $\frac{4mg\sin \theta }{3K}$