Question:
A wheel having moment of inertia $2\,kg-m^2$ about its vertical axis, rotates at the rate of $60$ rpm about this axis. The torque which can stop the wheel's rotation in one minute would be
A wheel having moment of inertia $2\,kg-m^2$ about its vertical axis, rotates at the rate of $60$ rpm about this axis. The torque which can stop the wheel's rotation in one minute would be
Updated On: Jul 12, 2022
- $\frac{2\pi}{15} N-m$
- $\frac{\pi}{12} N-m$
- $\frac{\pi}{15} N-m$
- $\frac{\pi}{18} N-m$
Hide Solution
Verified By Collegedunia
The Correct Option is C
Solution and Explanation
Given, $I=2 \,kg - m ^{2}, \omega_{0}=\frac{60}{60} \times 2 \pi\, rad / s$
$\omega=0, t=60\, s$
The torque required to stop the wheel's rotation is
$\tau=I \alpha=I\left(\frac{\omega_{0}-\omega}{t}\right) $
$\therefore \tau=\frac{2 \times 2 \pi \times 60}{60 \times 60}$
$=\frac{\pi}{15} N - m$
Was this answer helpful?
0
0
Top Questions on System of Particles & Rotational Motion
- During an elastic collision between two bodies, which of the following statements are correct?
- KCET - 2025
- Physics
- System of Particles & Rotational Motion
- The temperature of a body in air falls from \( 40^\circ \text{C} \) to \( 24^\circ \text{C} \) in 4 minutes. The temperature of the air is \( 16^\circ \text{C} \). The temperature of the body in the next 4 minutes will be:
- JEE Main - 2025
- Physics
- System of Particles & Rotational Motion
- The center of mass of a thin rectangular plate (fig - x) with sides of length \( a \) and \( b \), whose mass per unit area (\( \sigma \)) varies as \( \sigma = \sigma_0 \frac{x}{ab} \) (where \( \sigma_0 \) is a constant), would be
- JEE Main - 2025
- Physics
- System of Particles & Rotational Motion
- Two iron solid discs of negligible thickness have radii \( R_1 \) and \( R_2 \) and moment of inertia \( I_1 \) and \( I_2 \), respectively. For \( R_2 = 2R_1 \), the ratio of \( I_1 \) and \( I_2 \) would be \( \frac{1}{x} \), where \( x \) is:
- JEE Main - 2025
- Physics
- System of Particles & Rotational Motion
- The moment of inertia of a solid disc rotating along its diameter is 2.5 times higher than the moment of inertia of a ring rotating in a similar way. The moment of inertia of a solid sphere which has the same radius as the disc and rotating in similar way, is \( n \) times higher than the moment of inertia of the given ring. Here, \( n = \):
- JEE Main - 2025
- Physics
- System of Particles & Rotational Motion
View More Questions
Concepts Used:
System of Particles and Rotational Motion
- The system of particles refers to the extended body which is considered a rigid body most of the time for simple or easy understanding. A rigid body is a body with a perfectly definite and unchangeable shape.
- The distance between the pair of particles in such a body does not replace or alter. Rotational motion can be described as the motion of a rigid body originates in such a manner that all of its particles move in a circle about an axis with a common angular velocity.
- The few common examples of rotational motion are the motion of the blade of a windmill and periodic motion.