Question

A block of mass $10\text{kg}$ is suspended from a string of length $4\text{m}$. When pulled by a force $F$ along the horizontal from its midpoint, upper half of the string makes an angle ${45}^{\circ }$ with the vertical. The value of $F$ is

• A. $100\text{N}$
• B. $90\text{N}$
• C. $75\text{N}$
• D. $70\text{N}$

Answer 1

The correct option is A $100\text{N}$


System is in equilibrium. Hence, $\sum F_y=0$
$T\cos {45}^{\circ }-100=0$
or $\frac{T}{\sqrt{2}}=100$ .....(i)
and $\sum F_y=0$
$T\sin {45}^{\circ }-F=0$
or $\frac{T}{\sqrt{2}}=F$ ....(ii)
From eqn (i) and (ii)
$F=100\text{N}$