Question
Medium
Solving time: 3 mins
A stationary horizontal disc is free to rotate about its axis. When a torque is applied on it, its kinetic energy as a function of , where is the angle by which it has rotated, is given as . If its moment of inertia is , then the angular acceleration of the disc is (a) (b) (c) (d)
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Text solutionVerified
Exp. (d)
Given, kinetic energy
We know that, kinetic energy of a rotating body about its axis
where, is moment of inertia and is angular velocity.
So,
or
Differentiating the above equation w.r.t. time on both sides, we get
Angular acceleration, [using Eq. (i)] or
Alternate Solution
As,
or
or
Given, kinetic energy
We know that, kinetic energy of a rotating body about its axis
where, is moment of inertia and is angular velocity.
So,
or
Differentiating the above equation w.r.t. time on both sides, we get
Angular acceleration, [using Eq. (i)] or
Alternate Solution
As,
or
or
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Question Text | A stationary horizontal disc is free to rotate about its axis. When a torque is applied on it, its kinetic energy as a function of , where is the angle by which it has rotated, is given as . If its moment of inertia is , then the angular acceleration of the disc is
(a)
(b)
(c)
(d) |
Updated On | Mar 4, 2023 |
Topic | System of Particles and Rotational Motion |
Subject | Physics |
Class | Class 11 |
Answer Type | Text solution:1 Video solution: 2 |
Upvotes | 202 |
Avg. Video Duration | 2 min |