A pulley has the shape of a uniform solid disc of mass 2 kg and radius 0.5 m. A string is wrapped over its rim and is pulled by a force of 2.5 N. The pulley is free to rotate about its axis. Initially, the pulley is at rest. Find the angular velocity of pulley just after 10 s.

Question

A pulley has the shape of a uniform solid disc of mass 2 kg and radius 0.5 m. A string is wrapped over its rim and is pulled by a force of 2.5 N. The pulley is free to rotate about its axis. Initially, the pulley is at rest. Find the angular velocity of pulley just after 10 s. (A) 20 rad/s (B) 100 rad/s (C) 40 rad/s (D) 50 rad/s

Tardigrade Admin · Accepted Answer

<img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/physics/99e505f50d5910611666a8523b25f822-.png" /> Moment of inertia of pulley I =(1/2) mR 2=(1/2) × 2 ×(0.5)2=0.25 kg m 2 Torque produced by force about O τ0=2.5 × 0.5= I α=0.25 α α=5 rad / s 2( constant ) ω=ω0+α t =0+5 × 10=50 rad / s

Q. A pulley has the shape of a uniform solid disc of mass $2 k g$ and radius $0.5 m$ . A string is wrapped over its rim and is pulled by a force of $2.5 N$ . The pulley is free to rotate about its axis. Initially, the pulley is at rest. Find the angular velocity of pulley just after $10 s$ .

20 rad/s

100 rad/s

40 rad/s

50 rad/s

Moment of inertia of pulley
$I = \frac{1}{2} m R^{2} = \frac{1}{2} \times 2 \times (0.5)^{2} = 0.25 k g m^{2}$
Torque produced by force about $O$
$τ_{0} = 2.5 \times 0.5 = I α = 0.25 α$
$α = 5 r a d / s^{2} ($ constant $)$
$ω = ω_{0} + α t = 0 + 5 \times 10 = 50 r a d / s$

Q. A pulley has the shape of a uniform solid disc of mass 2kg and radius 0.5m. A string is wrapped over its rim and is pulled by a force of 2.5N. The pulley is free to rotate about its axis. Initially, the pulley is at rest. Find the angular velocity of pulley just after 10s.