A ball of mass \(1\, kg\) and radius \(0.5\, m,\) starting from test rolls down on a \(30^{\circ}\) inclined plane. The torque acting on the ball at the distance of the \(7\, m\) from the starting point is close to
(Take: Acceleration due to gravity as \(10\, m/s^2\))
(Take: Acceleration due to gravity as \(10\, m/s^2\))
- 0.25 N-m
- 0.7 N-m
- 0.5 N-m
- 0.4 N-m
The Correct Option is B
Solution and Explanation
Given, ball of mass \(M=1\, kg\),
Radius of ball \(R=0.5\,m\),
Angle of inclination \(\theta=30^{\circ}\)
A ball placed on a inclined plane.
Acceleration of ball,
\(a=\frac{g \sin \theta}{1+\frac{I}{M R^{2}}}\)
Where, \(I=\) moment of inertia of ball
\(\Rightarrow a=\frac{10 \times \sin 30^{\circ}}{1+\frac{2}{5} \frac{M R^{2}}{M R^{2}}}=\frac{5 \times 5}{7}\)
Torque on the ball \(\tau=I \alpha=I \frac{a}{R}\)
\(\Rightarrow \tau =\frac{2}{5} M R^{2}\left[\frac{5 \times 5}{7}\right] \frac{1}{R}\)
\(\Rightarrow \tau =\frac{2}{5} \times 1 \times 0.5 \times \frac{5 \times 5}{7}\)
\(\Rightarrow \tau =\frac{5}{7}=0.71\, N - m\)
So, the correct option is (B): \(0.7 \ N-m\)
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Concepts Used:
Torque
Torque is a moment of force. Torque is measured as a force that causeque is also defined as the turning effect of force on the axis of rotation. Torque is chs an object to rotate about an axis and is responsible for the angular acceleration. Characterized with “T”.
How is Torque Calculated?
Torque is calculated as the magnitude of the torque vector T for a torque produced by a given force F
T = F. Sin (θ)
Where,
r - length of the moment arm,
θ - the angle between the force vector and the moment arm.
Read More: Torque
Types of Torque
Torque is of two types:
- Static torque
- Dynamic torque