(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

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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, $g = 10 \ m/s^2$)

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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, $g = 10 \ m/s^2$)

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$A$ truck is moving at a speed of $54 \ km/h$. The radius of its wheels is $50 \ cm$. If the wheels come to rest after $20$ rotations upon applying brakes,what is the linear distance covered by the truck during this time? What is the angular acceleration of the wheels?

Let $\vec{A}$ be a unit vector along the axis of rotation of a purely rotating body and $\vec{B}$ be a unit vector along the velocity of a particle $P$ of the body away from the axis. The value of $\vec{A} \cdot \vec{B}$ is

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 $\alpha_2$.

$A$ wheel of radius $1.5 \ m$ rotates with a constant angular acceleration of $10 \ rad/s^2$. Its initial angular speed is $(\frac{60}{\pi}) \ rpm$. What will be its angular speed and angular displacement at $t = 2.0 \ s$?

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