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-
- \(\sqrt {2gh}\)
- \(\sqrt {\frac {3}{4gh}}\)
- \(\sqrt {\frac {4}{3}gh}\)
- \(\sqrt {4gh}\)
The Correct Option is C
Solution and Explanation
\(mgh=\frac {1}{2}mv^2(1+\frac {K^2}{R^2})\)
\(⇒ v =\sqrt {\frac {2gh}{(1+\frac {K^2}{R^2})}}\)
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Concepts Used:
Rotational Motion
Rotational motion can be defined as the motion of an object around a circular path, in a fixed orbit.
Rotational Motion Examples:
The wheel or rotor of a motor, which appears in rotation motion problems, is a common example of the rotational motion of a rigid body.
Other examples:
- Moving by Bus
- Sailing of Boat
- Dog walking
- A person shaking the plant.
- A stone falls straight at the surface of the earth.
- Movement of a coin over a carrom board
Types of Motion involving Rotation:
- Rotation about a fixed axis (Pure rotation)
- Rotation about an axis of rotation (Combined translational and rotational motion)
- Rotation about an axis in the rotation (rotating axis)