Question

In order to raise a mass of 100kg a man of mass 60 kg fastens a rope to it and passes the rope over a smooth pulley. He climbs the rope with an acceleration $\frac{5g}{4}$ relative to rope. The tension in the rope is $(g=10m{s}^{-2})$:

• A. 1432 N
• B. 928N
• C. 1218 N
• D. 642 N

Answer 1

The correct option is C 1218 N

For mass 100 g, $T-100g=100a....\left(1\right)$
$a=\frac{T}{100}-g$
For man, $60(\frac{5g}{4}-a)=T-60g....\left(2\right)$
putting the value of a in eqn (2), we get,
$60(g-\frac{T}{100}+\frac{5g}{4})=T-60g$
$60g-\frac{3}{5}T+75g=T-60g$
$195g=\frac{8}{5}T$
$T=\frac{9750}{8}=1218N$