Question

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

• A. $1550N$
• B. $1700N$
• C. $2100N$
• D. $1350N$

Answer 1

The correct option is D $1350N$

From figure, $T-Mg={Ma}^1⟶\left(1\right)$$T-mg=ma⟶\left(2\right)$

where $M=100$kg

$m=60$kg

$a^1=$ acceleration of block

$a=\frac{5g}{4}$

$\therefore \left(2\right)\Rightarrow T=ma+mg$

$F=m(a+g)$

$=60(g+\frac{5g}{4})$

$=\frac{60\times 9g}{4}$

$=\frac{5400}{4}$

$=1350N$.