A force of 49 N acts tangentially at the highest point of a sphere (solid) of mass 20 kg, kept on a rough horizontal plane. If the sphere rolls without slipping, then the acceleration of the center of the sphere is
A force of 49 N acts tangentially at the highest point of a sphere (solid) of mass 20 kg, kept on a rough horizontal plane. If the sphere rolls without slipping, then the acceleration of the center of the sphere is
Show Hint
- 3.5 \( m/s^2 \)
- 0.35 \( m/s^2 \)
- 2.5 \( m/s^2 \)
- 0.25 \( m/s^2 \)
The Correct Option is A
Solution and Explanation
Torque about bottom point: \( F \times 2r = I\alpha \)
\( 49 \times 2r = \frac{7}{5}mr^2\alpha \) \( 14 - 4r\alpha \)
As sphere rolls without slipping \( a = r\alpha \) \( a = \frac{14}{4} = \frac{7}{2} = 3.5 m/s^2 \)
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