Solve the following :


The door of an almirah is $6 \mathrm{ft}$ high, $1.5 \mathrm{ft}$ wide and weighs $8 \mathrm{~kg}$. The door is supported by two hinges situated at a distance of $1 \mathrm{ft}$ from the ends. If the magnitudes of the force exerted by the hinges on the door are equal, find this magnitude.


Magnitude of forces by hinges are equal.



Rotational Equilibrium at point $O$

$N_{4}(4)=8 g\left(\frac{1.5}{2}\right)$

$N_{4}=1.5 \mathrm{~g}$

Bv translational Equilibrium

$N_{3}=N_{4}=1.5 g$-(ii)

$N_{1}+N_{2}=8 g$

Solving (i),(ii),(iii)

$N_{1}=N_{2}=4 g$

Magnitude of force $=\sqrt{N_{1}^{2}+N_{4}^{2}}$

$=\sqrt{(4 g)^{2}+(1.5 g)^{2}}$

$=43 \mathrm{~N}$


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