(A) For the falling body of mass $m$,the equation of motion is:$mg - T = ma$ --- $(i)$For the rotating disc of mass $M$ and radius $R$,the torque equ

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(A) For the falling body of mass $m$,the equation of motion is:$mg - T = ma$ --- $(i)$For the rotating disc of mass $M$ and radius $R$,the torque equation is:$RT = I\alpha$Since $I = \frac{1}{2}MR^2$ and $\alpha = \frac{a}{R}$,we have:$RT = (\frac{1}{2}MR^2)(\frac{a}{R}) = \frac{1}{2}MRa$$T = \frac{Ma}{2}$ --- $(ii)$Substituting equation $(ii)$ into equation $(i)$:$mg - \frac{Ma}{2} = ma$$mg = ma + \frac{Ma}{2} = a(m + \frac{M}{2}) = a(\frac{2m + M}{2})$$a = \frac{2mg}{2m + M}$

Class 11 Physics System of Particles and Rotational Motion Rotation Motion Basic, Motion of Connected Mass

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$A$ uniform disc of radius $R$ and mass $M$ is free to rotate only about its axis. $A$ string is wrapped over its rim and a body of mass $m$ is tied to the free end of the string as shown in the figure. The body is released from rest. Then the acceleration of the body is

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$\frac{2mg}{2m + M}$
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$\frac{2Mg}{2m + M}$
C
$\frac{2mg}{2M + m}$
D
$\frac{2Mg}{2M + m}$

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System of Particles and Rotational Motion

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Rotation Motion Basic, Motion of Connected Mass

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$A$ uniform disc of radius $R$ and mass $M$ is free to rotate only about its axis. $A$ string is wrapped over its rim and a body of mass $m$ is tied to the free end of the string as shown in the figure. The body is released from rest. Then the acceleration of the body is

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As shown in the figure,a mass $m = 500 \ g$ hangs from the rim of a wheel of radius $r = 20 \ cm$. When released from rest,the mass falls $2.0 \ m$ in $8 \ s$. Then the moment of inertia of the wheel is .......... $kg \cdot m^2$. $(g = 10 \ m/s^2)$

$A$ ball of mass $m$ is released from inside a smooth wedge of mass $m$ as shown in the figure. What is the speed of the wedge when the ball reaches point $B$?

$A$ string is wrapped around a disc of mass $M$ and radius $R$ and the free end is fixed to the ceiling. The centre of mass falls down as the disc unwinds the string. The tension in the string is

$A$ rigid body is rotating with variable angular velocity $\omega = (a - bt)$ at any instant of time $t$. The total angle subtended by it before coming to rest will be ($a$ and $b$ are constants).

$A$ mass $m$ is supported by a massless string wound around a uniform hollow cylinder of mass $m$ and radius $R$. If the string does not slip on the cylinder,with what acceleration will the mass fall on release?

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