Question

A man of mass $60kg$ standing on a light weighting machine kept ina box of mass $30kg.$ The box is hanging from a pulley fixed to the ceiling through a light rope$,$ the other end of which is held by the man himself$.$ If the manages to keep the box at rest $\left(1\right)$ what is weight shown by the machine ? $\left(2\right)$ what force should the man exert on the rope to get his correct weight on the machine ?

• A. 150 N
• B. 300 N
• C. 600 N
• D. 900 N

Answer 1

The correct option is D 900 N

Let the tension force be $T$ in the rope$.$ The downward forces acting on the system of the man and the box are the weight of the man and the weight of the box$.$ The upward forces are $T$ and $T$ on each side of the rope$.$

As the system is in a static equilibrium$:$

$T+T=(60+30)g$

$=>T=45kgf$ or $45g$ $Newtons=450N$ if $g=10m/s^2$

The forces acting on the man are: Tension T, reaction from the weighing machine, and weight 60 g. So,

Normal$-$reaction of the weighing machine $=60-T=15kgf.$

$\left(i\right)$ The weighing machine shows its normal reaction force as the weight of the person standing on it$.$ So weight displayed $=15kg.$

$\left(ii\right)$ Suppose the man pulls down the rope with a force $F$ and the tension becomes $T$.

The forces acting downwards on the rope at the two ends are: F, weights of man and the box. The upward forces are Tension T on each side of rope.

The system being in equilibrium$:2T=F+60kgf+30kgf=F+90kgf$

$=>T=45kgf+F/2$

$=>$ Normal reaction force from the weighing machine on the man

$N=60+F-T=15kgf+F/2$

If N is to become $60kgf,$ then F has to be $90kgf$ or $900N$

Hence,

option $\left(D\right)$ is correct answer.