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Standard XII

Physics

Pendulum in Non Inertial Frame

Thin threads ...

Question

Thin threads are tightly wound on the ends of a uniform solid cylinder of mass $m$ . The free ends of the threads are attached to the ceiling of an elevator car. The car starts going up with an acceleration $_{0}$ .
Find the acceleration ${\to w}^{'}$ of the cylinder relative to the car :

{\to w}^{'} = \frac{2}{3} (g -_{0})

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{\to w}^{'} = \frac{3}{2} (g -_{0})

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{\to w}^{'} = 2 \frac{3}{2} (g -_{0})

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{\to w}^{'} = 2 \frac{2}{3} (g -_{0})

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Solution

The correct option is A ${\to w}^{'} = \frac{2}{3} (g -_{0})$
If the observer is in the elevator the gravitational force as
observed by the observer will be = $m (g - w_{o})$
where g= acceleration due to gravity $w_{o}$ = acceleration of the elevator
From Newton's Laws :
$m (g - w_{o}) - 2 T = m a$ .......(1) a = acceleration of the cylinder relative to the car
(because the observer is in the car he will see relative motion)
As slipping is not there:
$I α = 2 T r \frac{1}{2} m r^{2} * \frac{a}{r} = 2 T r T = \frac{m a}{54}$
Substitutung the value of T in equation (1)
$m (g - w_{o}) - \frac{m a}{2} = m a$
on solving we get
$\frac{3 m a}{2} = m (g - w_{o})$
or a= $\frac{2}{3} (g - w_{o})$

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Similar questions

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Thin threads are tightly wound on the ends of a uniform solid cylinder of mass m. The free ends of the threads are attached to the ceiling of an elevator car. The car starts going up with an acceleration →w0.Find the acceleration →w′ of the cylinder relative to the car :

Thin threads are tightly wound on the ends of a uniform solid cylinder of mass $m$ . The free ends of the threads are attached to the ceiling of an elevator car. The car starts going up with an acceleration $_{0}$ .
Find the acceleration ${\to w}^{'}$ of the cylinder relative to the car :