First slide

Torque

Question

Two wheels A and B of same mass are rotating with same angular velocity about their respective geometrical axis. Wheel A has radius R and wheel B has radius 2R. Same breaking torque is applied on the wheels. If wheel A stops in 1 minute, wheel B will stop in

Moderate

A

4 min.
B

2 min.
C

0.5 min.
D

6 min

Solution

(1)
$α = a n g u l a r r e t a r d a t i o n$
$\begin{array}{l} = \frac{τ}{\frac{1}{2} m r^{2}} = - \frac{2 τ}{m r^{2}} \\ U \sin g ω = ω_{0} - α t, \\ O = ω_{0} - (\frac{2 τ}{m r^{2}}) t \\ \Rightarrow t = \frac{ω_{0} m r^{2}}{2 τ} \\ \Rightarrow t α r^{2} \\ ∴ \frac{t_{B}}{t_{A}} = {(\frac{2 R}{R})}^{2} = 4 \Rightarrow t_{B} = 4 \times 1 \min = 4 \min . \end{array}$

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