Question

A man climbs a light rope whose breaking strength is $\eta$ times his weight $(\eta <1)$. The maximum acceleration of the man so that the rope just breaks is

• A. $g(1-\eta )$
• B. $g(1+\eta )$
• C. $g\eta$
• D. $\frac{g}{\eta }$

Answer 1

The correct option is A $g(1-\eta )$

FBD of man

Let the man accelerate in upward direction

$T-mg=ma$
$T=mg+ma$
Given $T=\eta mg$, is the maximum tention that the rope can withstand
$\eta mg=mg+ma$
$a=(\eta -1)g$

Here we get acceleration as negative as $\eta <1$ hence the man should accelerate in opposite to the assumed direction