Question:
A solid cylinder is released from rest from the top of an inclined plane of inclination 30° and length 60 cm If the cylinder rolls without slipping, its speed upon reaching the bottom of the inclined plane is ________ $ms ^{-1}$(Given $g =10 \,ms ^{-2}$ )
A solid cylinder is released from rest from the top of an inclined plane of inclination 30° and length 60 cm If the cylinder rolls without slipping, its speed upon reaching the bottom of the inclined plane is ________ $ms ^{-1}$(Given $g =10 \,ms ^{-2}$ )
Updated On: Mar 19, 2025
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Correct Answer: 2
Solution and Explanation
\[ v = \sqrt{\frac{2gh}{1 + \frac{k^2}{R^2}}} \] Where \( h = 60 \sin 30^\circ = 30 \) cm \[ k^2 = \frac{R^2}{2} \] \[ v = 2 \text{ ms}^{-1} \]
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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)