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The minimum acceleration with which a fireman can slide down a rope of breaking strength two-third of his weight is
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Verified Answer
The correct answer is:
$\frac{g}{3}$
If fireman slides down with some acceleration then its apparent weight decreases. For critical condition rope can bear only $\frac{2}{3}$ of the fireman's weight. Let $a$ is the minimum acceleration then,
Tension in the rope $=m(g-a)=$ Breaking strength
$$
\begin{array}{ll}
\Rightarrow & m(g-a)=\frac{2}{3} m g \\
\Rightarrow &=g-\frac{2 g}{3}=\frac{g}{3}
\end{array}
$$
Tension in the rope $=m(g-a)=$ Breaking strength
$$
\begin{array}{ll}
\Rightarrow & m(g-a)=\frac{2}{3} m g \\
\Rightarrow &=g-\frac{2 g}{3}=\frac{g}{3}
\end{array}
$$
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