(A) For the hanging mass $m$,the equation of motion is:$m g - T = m a$ --- $(1)$For the pulley,the torque equation is:$\tau = I \alpha$$T R = (\frac{

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(A) For the hanging mass $m$,the equation of motion is:$m g - T = m a$ --- $(1)$For the pulley,the torque equation is:$\tau = I \alpha$$T R = (\frac{1}{2} m R^2) \alpha$Since the string does not slip,$a = R \alpha$,so $\alpha = \frac{a}{R}$.$T R = \frac{1}{2} m R^2 (\frac{a}{R})$$T = \frac{m a}{2}$ --- $(2)$Substituting equation $(2)$ into equation $(1)$:$m g - \frac{m a}{2} = m a$$m g = m a + \frac{m a}{2}$$m g = \frac{3 m a}{2}$$a = \frac{2}{3} g$

Class 11 Chemistry Data Entry - Chemistry Level 0 of all question bank

$A$ mass $m$ hangs with the help of a string wrapped around a pulley on a frictionless bearing. The pulley has mass $m$ and radius $R$. Assuming the pulley to be a perfect uniform circular disc,the acceleration of the mass $m$,if the string does not slip on the pulley,is:

AIEEE 2011 All AIEEE

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$\frac{2}{3} g$
B
$\frac{g}{3}$
C
$\frac{3}{2} g$
D
$g$

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$A$ mass $m$ hangs with the help of a string wrapped around a pulley on a frictionless bearing. The pulley has mass $m$ and radius $R$. Assuming the pulley to be a perfect uniform circular disc,the acceleration of the mass $m$,if the string does not slip on the pulley,is:

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$A$ uniform beam of weight $W$ is attached to a vertical wall by a hinge $H$. The beam is held horizontal by a rope as shown below. Which one of the following best shows the direction of the reaction force $R$ at the hinge?

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