(C) For linear motion: $Mg - 2T = Ma$ For rotational motion: $2TR = I\alpha$ Here,$I = \frac{MR^2}{2}$ and $\alpha = \frac{a}{R}$. Substituting these

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(C) For linear motion: $Mg - 2T = Ma$ For rotational motion: $2TR = I\alpha$ Here,$I = \frac{MR^2}{2}$ and $\alpha = \frac{a}{R}$. Substituting these into the torque equation: $2TR = (\frac{MR^2}{2})(\frac{a}{R}) \implies 2TR = \frac{MRa}{2} \implies T = \frac{Ma}{4}$. Substituting $T$ into the linear motion equation: $Mg - 2(\frac{Ma}{4}) = Ma \implies Mg - \frac{Ma}{2} = Ma \implies Mg = \frac{3Ma}{2} \implies a = \frac{2}{3}g$. Now,find the tension $T$: $T = \frac{M}{4}(\frac{2}{3}g) = \frac{Mg}{6}$.

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

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$A$ solid cylinder of mass $M$ and radius $R$ is placed in a horizontal position. Two strings are wrapped around the cylinder. Find the tension in the strings and the acceleration of the cylinder as the strings unwind.

A
$Mg, 4g$
B
$\frac{Mg}{2}, \frac{4}{3}g$
C
$\frac{Mg}{6}, \frac{2}{3}g$
D
$\frac{Mg}{3}, \frac{1}{3}g$

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System of Particles and Rotational Motion

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Rotation Motion Basic, Motion of Connected Mass

$A$ uniform disc of radius $R$ and mass $M$ can rotate on a smooth axis passing through its centre and perpendicular to its plane. $A$ force $F$ is applied on its rim as shown in the figure. What is the tangential acceleration of the rim?

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The direction of the angular velocity vector is along which of the following?

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$A$ uniform solid cylinder of mass $M$ and radius $R$ rotates about a frictionless horizontal axle. Two similar masses $m$ are suspended with the help of two ropes wrapped around the cylinder. If the system is released from rest,then the acceleration of each mass will be

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In the given figure,the linear acceleration of the solid cylinder of mass $m_2$ is $a_2$. Then,its angular acceleration $\alpha_2$ is (given that there is no slipping):

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In the given figure,the linear acceleration of the solid cylinder of mass $m_2$ is $a_2$. If there is no slipping,find its angular acceleration $\alpha_2$.

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$A$ solid cylinder of mass $M$ and radius $R$ is placed in a horizontal position. Two strings are wrapped around the cylinder. Find the tension in the strings and the acceleration of the cylinder as the strings unwind.

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$A$ uniform disc of radius $R$ and mass $M$ can rotate on a smooth axis passing through its centre and perpendicular to its plane. $A$ force $F$ is applied on its rim as shown in the figure. What is the tangential acceleration of the rim?

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