A solid cylinder length is suspended symmetrically through two massless strings, as shown in the figure. The distance from the initial rest position, the cylinder should be unbinding the strings to achieve a speed of 4 m/s, is ______ cm. (Take g = 10 m/s2).
Fig.
A solid cylinder length is suspended symmetrically through two massless strings, as shown in the figure. The distance from the initial rest position, the cylinder should be unbinding the strings to achieve a speed of 4 m/s, is ______ cm. (Take g = 10 m/s2).
Correct Answer: 120
Solution and Explanation
The correct answer is 120
\(α = \frac{(mg)(r)}{\frac{3}{2}mr^2} = \frac{2g}{3r}\)
\(⇒ a = \frac{2g}{3}\)
\(⇒ v^2 = 2as\)
\(16 = \frac{40}{3}×s\)
⇒ s = 0.3×4
= 120cm
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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)