Consider the door of a room of wieght `W` hinged at two points as shown in the diagram. If the magnitude of forces by the hings on the door are equal, find the magnitude of force.

Explanation

The forces acting on hinges are as shown

Since the door is in equilibrium
`Sigma F_(x)=0impliesH_(2)=H_(1)`
`Sigma F_(y)=0impliesV_(1)+V_(2)=W`
`Sigma tau_(2)=0impliesH_(1)xx2L+Wxx(L)/(2)=0`
`H_(1)=-(W)/(4)`
That is, the direction of `H_(1)` is opposite to the direction shown in the figure. Reaction on hinges are equal in magnitude
`R_(1) = R_(2)`
`sqrt(H_(1)^(2)+V_(1)^(2))=sqrt(H_(2)^(2)+V_(2)^(2))impliesV_(1)=V_(2)=(W)/(2)`
Reaction on hinges
`R_(1)=R_(2)=sqrt(H_(1)^(2)+V_(1)^(2))=sqrt(((W)/(4))^(2)+((W)/(2))^(2))=(sqrt5W)/(4)`