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The system of two masses $2 \mathrm{~kg}$ and $3 \mathrm{~kg}$ as shown in the figure is released from rest. The work done on $3 \mathrm{~kg}$ block by the force of gravity during first 2 seconds of its motion is $\left(g=10 \mathrm{~ms}^{-2}\right)$
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Verified Answer
The correct answer is:
$120 \mathrm{~J}$
This is the example of Atwood machine, so acceleration is the system
$$
\begin{aligned}
a & =\left(\frac{M-m}{M+m}\right) g \\
a & =\frac{1}{5} \times 10=2 \mathrm{~m} / \mathrm{s}^2 \\
s & =u t+\frac{1}{2} a t^2=0+\frac{1}{2} \times 2\left(2^2\right. \\
s & =4 \mathrm{~m}
\end{aligned}
$$
Now,
$$
\Rightarrow \quad s=4 \mathrm{~m}
$$
Work done on block of $3 \mathrm{~kg}$ by gravity
$$
\begin{aligned}
& W=M g s=3 \times 10 \times 4 \\
& W=120 \mathrm{~J}
\end{aligned}
$$
$$
\begin{aligned}
a & =\left(\frac{M-m}{M+m}\right) g \\
a & =\frac{1}{5} \times 10=2 \mathrm{~m} / \mathrm{s}^2 \\
s & =u t+\frac{1}{2} a t^2=0+\frac{1}{2} \times 2\left(2^2\right. \\
s & =4 \mathrm{~m}
\end{aligned}
$$
Now,
$$
\Rightarrow \quad s=4 \mathrm{~m}
$$
Work done on block of $3 \mathrm{~kg}$ by gravity
$$
\begin{aligned}
& W=M g s=3 \times 10 \times 4 \\
& W=120 \mathrm{~J}
\end{aligned}
$$
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