The door of an almirah is 6ft high, 1.5ft wide and weighs 8kg. The door is supported by two hinges situated at a distance of 1ft from the ends. If the magnitudes of the forces exerted by the hinges on the door are equal, find this magnitude.
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According to the question
$8 g=F_1+F_2 ; N_1=N_2$
Since, $R_1=R_2$
Therefore $\mathrm{F}_1=\mathrm{F}_2$
$\Rightarrow 2 \mathrm{~F}_1=8 \mathrm{~g}$
$\Rightarrow \mathrm{~F}_1=40$
Let us take torque about the point B , we will get $\mathrm{N}_1 \times 4=8 \mathrm{~g} \times 0.75$.
$\Rightarrow\text{N}_1=\frac{(80\times3)}{(4\times4)}=15\text{N}$
Therefore $\sqrt{\Big(\text{F}_1^2+\text{N}_1^2\Big)}=\text{R}_1$
$\sqrt{40^2+15^2}=42.72=43\text{N.}$
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