First slide

Torque

Question

A block of mass m, connected to a light string wrapped over a disc pulley of mass 2 m and radius 2r, is being pulled by a constant horizontal force F as shown. Tangential acceleration of a point distant r from the axis of pulley is (Assume that there is no slipping between the string and the pulley)

Moderate

A

$\frac{F}{m}$
B

$\frac{F}{2 m}$
C

$\frac{F}{4 m}$
D

$\frac{2 F}{3 m}$

Solution

$F - T = ma$
$T \times 2 r = 2 m \times \frac{4 r^{2}}{2} \times \frac{a}{2 r}$
$F = 2 ma$
$a_{t} = \frac{F}{2 m} = α \times 2 r$
$α = \frac{F}{4 mr}$
${(a_{t})}_{r} = α r = \frac{F}{4 mr} \times r$
$= \frac{F}{4 m}$

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