Question

A thin rod of mass $m$ and length $2 l$ is made to rotate about an axis passing through its centre and perpendicular to it. If its angular velocity changes from 0 to $\omega$ in time $t$, the torque acting on it is (a) $\frac{m l^{2} \omega}{12 t}$ (b) $\frac{m l^{2} \omega}{3 t}$ (c) $\frac{m l^{2} \omega}{t}$ (d) $\frac{4 m l^{2} \omega}{3 t}$

Name: Problem 67, Chapter 7: Objective Physics for NEET
Uploaded: 2021-09-12T17:17:18-08:00
Duration: 1 min 48 s
Channel: Akhil K
Description: A thin rod of mass m and length 2 l is made to rotate about an axis passing through its centre and perpendicular to it. If its angular velocity changes from 0 to ωin time t, the torque acting on it is (a) (m l^2 ω)/(12 t) (b) (m l^2 ω)/(3 t) (c) (m l^2 ω)/(t) (d) (4 m l^2 ω)/(3 t)

   A thin rod of mass $m$ and length $2 l$ is made to rotate about an axis passing through its centre and perpendicular to it. If its angular velocity changes from 0 to $\omega$ in time $t$, the torque acting on it is
(a) $\frac{m l^{2} \omega}{12 t}$
(b) $\frac{m l^{2} \omega}{3 t}$
(c) $\frac{m l^{2} \omega}{t}$
(d) $\frac{4 m l^{2} \omega}{3 t}$

Objective Physics for NEET

Abhay Kumar 1st Edition

Chapter 7, Problem 67

Instant Answer

Solved by Expert Akhil K

09/12/2021

Step 1

In this case, the length of the rod is $2l$, so the moment of inertia is $I = \frac{m (2l)^{2}}{12} = \frac{m l^{2}}{3}$. Show more…

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A thin rod of mass $m$ and length $2 l$ is made to rotate about an axis passing through its centre and perpendicular to it. If its angular velocity changes from 0 to $\omega$ in time $t$, the torque acting on it is (a) $\frac{m l^{2} \omega}{12 t}$ (b) $\frac{m l^{2} \omega}{3 t}$ (c) $\frac{m l^{2} \omega}{t}$ (d) $\frac{4 m l^{2} \omega}{3 t}$

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Key Concepts

Torque

Torque is the rotational analog of force. It is defined as the product of the moment of inertia and the angular acceleration of a rotating object. This concept is central to understanding how rotational motion is initiated and altered, akin to how force affects linear motion in Newton's second law.

Moment of Inertia

The moment of inertia quantifies an object's resistance to changes in its rotational motion. It depends on both the mass and the distribution of mass relative to the axis of rotation. A higher moment of inertia means that a given torque will produce a smaller angular acceleration.

Angular Acceleration

Angular acceleration is the rate at which the angular velocity of an object changes with time. It is analogous to linear acceleration in translational motion and is generated when a net torque is applied to a body. Angular acceleration is computed as the change in angular velocity divided by the change in time.

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