An object of mass 2 kg is hanging from a rop | vedclass

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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

Vedclass · Accepted Answer

$\frac{20}{3} \ m/s^2$

Vedclass · Answer

(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 $	au = 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 $T$: $20 - 2a = a \Rightarrow 3a = 20 \Rightarrow a = \frac{20}{3} \ m/s^2$.

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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