A uniform rod of length L and weight `W_(R)` is suspended as shown in the accompanying figure. A weight W is added to the end of the rod. The rod rests in horizontal position and is hinged at O. the support wire is at an angle `theta` to the rod. What is the tension T in the wire ?

Options

A. `T=W/(sin theta)`
B. `T=W+W_(R)`
C. `T=W+1//2W_(R)`
D. `T=(W+1//2W_(R))/(sin theta)`

Answer

D

Explanation

The forces on rod hinged at O, which causes torques about O are as shown
Since net torque on rod about hinge at O is zero
`T sin thetaxxl=W_(R)xxl/2+Wxxl`
or `T=((W_(R))/2+W)/(sin theta)`