First slide

Torque

Question

A uniform cylindrical disc of radius R and mass M is pulled over a horizontal friction less surface by a constant force. The force is applied by means of a string wound around the disc as shown in fig. (2).
If it starts from rest at t = O, the linear and angular displacements respectively at time , are

Moderate

A

$(\frac{F}{M}) t^{2}, (\frac{F}{MR}) t^{2}$
B

$(\frac{F}{2 M}) t, (\frac{F}{2 MR}) t^{2}$
C

$(\frac{F}{M}) t^{2}, (\frac{F}{M}) t^{2}$
D

$(\frac{2 F}{M}) t^{2}, (\frac{2 F}{MR}) t^{2}$

Solution

We know that, $τ = Iα = FR$
$∴ (\frac{1}{2} {MR}^{2}) α = FR or α = (\frac{2 F}{MR})$
Now, acceleration $a = αR = \frac{2 F}{M}$
The distance travelled $s = \frac{1}{2} {at}^{2} = \frac{1}{2} (\frac{2 F}{M}) t^{2}$
$s = (\frac{F}{M}) t^{2}$
Further $θ = \frac{1}{2} {αt}^{2} = \frac{1}{2} (\frac{2 F}{MR}) t^{2} = (\frac{F}{MR}) t^{2}$

Get Instant Solutions

When in doubt download our app. Now available Google Play Store- Doubts App

Recieve an sms with download link

Doubts App

OR

SCAN ME

Doubts App

Doubts App