Question

A rope of negligible mass is wound round a hollow cylinder of mass 3 kg and radius 40 cm. If the rope is pulled with a force of 30 N, then the angular acceleration produced in the cylinder is

• A. $15 \mathrm { rads } ^ { - 2 }$
• B. $20 \mathrm { rads } ^ { - 2 }$
• C. $25 \mathrm { rads } ^ { - 2 }$
• D. $30 \mathrm { rads } ^ { - 2 }$

Answer 1

Answer: (C)

$25 \mathrm { rads } ^ { - 2 }$

Answer 2

Here, M = 3 kg

R = 40 cm = 40 × $10 ^ { - 2 }$m

Force applied, F = 30 N

Torque,

$\tau = \mathrm { FR } = ( 30 \mathrm {~N} ) \left( 40 \times 10 ^ { - 2 } \mathrm {~m} \right) = 12 \mathrm { Nm }$

Moment of inertia of hollow cylinder about its axis is

Let $\alpha$ is the angular acceleration produced.

As: