Wedge Problem

Q. A solid cylinder of mass 'M' and radius 'R' rolls without slipping down an inclined plane of length 'L' and height 'h'. What is the speed of its centre of mass when the cylinder reaches its bottom

1. $\sqrt{\frac{3}{4}gh}$
2. $\sqrt{\frac{4}{3}gh}$
3. $\sqrt{4gh}$
4. $\sqrt{2gh}$

Q. A ring, solid sphere, and a disc are rolling down from the top of the same height, then the sequence to reach on surface is?

1. Ring, disc, sphere
2. Sphere, disc, ring
3. Disc, ring, sphere

4. Sphere, ring, disc

Q. A solid sphere of mass 0.1 kgand radius 2 cmrolls down an inclined plane 1.4min length at an angle whose slope is 1/10. If sphere started from rest, its final velocity will be

1. 1.4 m/sec
2. 0.14 m/sec
3. 14 m/sec
4. 0.7 m/sec

Q. A ring, solid sphere, and a disc are rolling down from the top of the same height, then the sequence to reach on surface is?

1. Ring, disc, sphere
2. Sphere, disc, ring
3. Disc, ring, sphere

4. Sphere, ring, disc

Q.

A solid cylinder rolls down a fixed inclined plane of height 'h' and inclination $\theta$. Calculate the time taken to reach bottom?

{Assume the mass be M and radius be R}

1. $\sqrt{\frac{3h}{gsin\theta }}$

2. $\sqrt{\frac{3hsin\theta }{g}}$

3. $\sqrt{\frac{3h}{g}}si{n}^2\theta$

4. $cosec\theta \sqrt{\frac{3h}{g}}$

Q. A solid sphere and a disc of same mass and radius starts rolling down a rough inclined plane, from the same height the ratio of the time taken in the two cases is

1. $15:14$
2. $\sqrt{15}:\sqrt{14}$
3. $14:15$
4. $\sqrt{14}:\sqrt{15}$