Question

The door of an almirah is $6ft$ high, $1.5ft$ wide and weights $8kg$. The door is supported by two hinges situated at a distance of 1 ft from the ends. Assuming force exerted on the hinges are equal, the magnitude of the force is :

• A. $15N$
• B. $10N$
• C. $28N$
• D. $43N$

Answer 1

The correct option is D $43N$

The door of an almirah is $6$ft high, $1.5$ft wide and weighs $8kg$. The door is supported by two hinges situated at distance of $1$ft from the ends. If the magnitudes of the forces exerted by the hinges on the door are equal find this magnitude.
We have
$CD=0.75ft=0.225m$
$AB=4.0ft=1.2m$
Let the force on the upper hinge A be $F_1$ and on the lower hinge B be $F_2$ with their respective vertical and horizontal components $f_1$ & $f_2$ and $N_1$ and $N_2$. By equating vertical and horizontal components of the net force on the hinges
We get
$N_1=N_2$
And $f_1+f_2=8ℊ$
Also $F_1=F_2$ read with above two relations gives us
$f_1=f_2=4ℊ=40N$
As the door does not rotate through an axis through B and perpendicular to line AB, the torque on hinge B about this axis is zero, we get
$0=\tau =-AB{N}_1+CD㎎=-1.2N_1+0.225㎎$
$\Rightarrow N_1=15$
Thus $F=\sqrt{{40}^2+{15}^2}=43N$