(D) Let the tension in the rope be $T$ and the acceleration of the block be $a$. For the block: $mg - T = ma \Rightarrow 2g - T = 2a \Rightarrow T = 2

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(D) Let the tension in the rope be $T$ and the acceleration of the block be $a$. For the block: $mg - T = ma \Rightarrow 2g - T = 2a \Rightarrow T = 2(g - a) = 2(10 - a) = 20 - 2a$. For the pulley: The torque $\tau = T \cdot R = I \alpha$. Since $I = \frac{1}{2}MR^2$ and $a = R\alpha$, we have $T \cdot R = (\frac{1}{2}MR^2) \cdot (\frac{a}{R}) = \frac{1}{2}Ma$. Given $M = 2 \ kg$, $T = \frac{1}{2} \cdot 2 \cdot a = a$. Equating the two expressions for $T$: $20 - 2a = a \Rightarrow 3a = 20 \Rightarrow a = \frac{20}{3} \ m/s^2$.

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

Difficult

An object of mass $2 \ kg$ is hanging from a rope that is wrapped around a pulley of radius $25 \ cm$. The mass of the pulley is $2 \ kg$. Find the acceleration of the object. (Assume the pulley to be a solid disk, $g = 10 \ m/s^2$)

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A
$\frac{2}{3} \ m/s^2$
B
$\frac{4}{3} \ m/s^2$
C
$\frac{10}{3} \ m/s^2$
D
$\frac{20}{3} \ m/s^2$

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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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An object of mass $2 \ kg$ is hanging from a rope that is wrapped around a pulley of radius $25 \ cm$. The mass of the pulley is $2 \ kg$. Find the acceleration of the object. (Assume the pulley to be a solid disk, $g = 10 \ m/s^2$)

Similar Questions

$A$ plank with a uniform sphere placed on it rests on a smooth horizontal plane. The plank is pulled to the right by a constant force $F$. If the sphere does not slip over the plank,which of the following is true?

$A$ table rotates about a vertical axis passing through its center with an angular velocity of $20\ rad/s$. $A$ flywheel is mounted on it,which rotates about a horizontal axis with an angular velocity of $40\ rad/s$. The resultant angular velocity of the flywheel is:

$A$ 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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