Question

A door $1.6\text{m}$ wide requires a minimum force of $1\text{N}$ to be applied at the free end to open or close it. The minimum force that is required at a point $0.4\text{m}$ away from the hinges for opening or closing the door is

• A. $1.2\text{N}$
• B. $2.4\text{N}$
• C. $3.6\text{N}$
• D. $4\text{N}$

Answer 1

The correct option is D $4\text{N}$

We know that, torque $\tau =F\times d$
From the question,
$\tau =1\times 1.6=1.6\text{Nm}$
So, when $d_1=0.4\text{m}$
$\tau =F_1\times d_1$
or $F_1=\frac{\tau }{d_1}=\frac{1.6}{0.4}=4\text{N}$