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  4. In order to raise a mass of 100 kg 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 (5 g/4) relative to the rope. The tension in the rope is near to (take g=10 m s- 2 )

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Q. In order to raise a mass of $100 \, kg$ 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 $\frac{5 g}{4}$ relative to the rope. The tension in the rope is near to (take $g=10 \, m \, s^{- 2}$ )

NTA AbhyasNTA Abhyas 2020Laws of Motion

Solution:

assume block of mass $100kg$ is moving upward with acceleration $a$ with respect to ground and tension in the rope is $T$ . Then,
for man
$T-60g=60\left(\frac{5 g}{4} - a\right)$ ....... $\left(\right.1\left.\right)$ ( $\because $ man is climbing on the rope with acceleration $\frac{5 g}{4}$ )
for block
$T-100g=100a$ ...... $\left(\right.2\left.\right)$
solving equation $\left(\right.1\left.\right)$ and $\left(\right.2\left.\right)$
$T=1218.7N\approx 1218N$