Question

Kamala tries to open a door by applying force of $3500\text{gf-cm}$ at the doorknob. If the knob is $60\text{cm}$ from the hinge, what force (in $\text{N}$) should she apply in order to open the door by pushing it at a distance of $25\text{cm}$ from the knob?

• A. 58.8

Answer 1

The correct option is A 58.8
Given:
Distance between the doorknob and the door hinge, ${\text{l}}_1=60\text{cm}$
Force applied at the doorknob, ${\text{F}}_1=3500\text{gf-cm}$
In the second case, force (say ${\text{F}}_2$) is applied at a distance of $25\text{cm}$ from the doorknob, i.e. it is applied at a distance of ${\text{l}}_2=60-25=35\text{cm}$ from the hinge.
According to the principle of moments,
${\text{F}}_1\times {\text{l}}_1={\text{F}}_2\times {\text{l}}_2$

$⟹{\text{F}}_2=\frac{{\text{F}}_1\times {\text{l}}_1}{{\text{l}}_2}$

$⟹{\text{F}}_2=\frac{3500\times 60}{35}=6000\text{gf}$
$1\text{kgf}=1000\text{gf}$
$⟹6000\text{gf}=\frac{6000}{1000}=6\text{kgf}$

Also, $1\text{kgf}=9.8\text{N}$
$⟹6\text{kgf}=6\times 9.8=58.8\text{N}$