Question

The minimum acceleration with which a fireman can slide down a rope of breaking strength two third of his weight is

• A. Zero
• B. $\frac{g}{3}$
• C. $\frac{2g}{3}$
• D. $g$

Answer 1

The correct option is B $\frac{g}{3}$

If the person freely gets suspended from the rope,the rope will break as then the tension in the rope will be equal to weight of the person. Thus in order to prevent the rope from breaking, the person should slide down the rope with an acceleration greater than a certain minimum.If T is the force with which the person pulls the rope downwards, T is also the force with which the rope pulls the person upwards.
Thus for the downward accelerated movement of the fireman, $mg-T=ma$
or, $mg-\frac{2}{3}mg=ma$
$a=\frac{g}{3}$