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In the figure a uniform rod of mass 'm' ...

In the figure a uniform rod of mass `'m'` and length `'l'` is hinged at one end and the other end is connected to a light vertical of spring constant `'k'` as shown in figure. The spring has extension such that rod is equilibrium when it is horizontal . The rod rotate about horizontal axis passing through end `'B'`. Neglecting friction at the hinge find `(a)` extension in the spring `(b)` the force on the rod due to hinge.

Text Solution

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The correct Answer is:
A, B
`(a)` net torque about `B=0`
`=mg. (l)/(2)=kx.l or x=(mg)/(2k)`

`(b)` For the rod to be in equilibrium net force on it `=0`
`=F_(x)=0`
`kx+F_(y)=mg`
`rArr F_(y)=(mg)/(2)`
Ans. `(a) (mg)/(2k) (b) (mg)/(2)`
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