Two blocks each of mass M are connected to the ends of a light frame as shown in figure. The frame si rotated about the vertical line of symmetry. The rod breaks if the tension in it exceeds `T_0`. Find the maximum frequency with which the frame may be rotted without breaking the rod.

Options

A. `(1)/(2pi)((To)/(2Ml))^(1//2)`
B. `(1)/(4pi)((To)/(Ml))^(1//2)`
C. `(1)/(2pi)((To)/(Ml))^(1//2)`
D. `(1)/(4)((To)/(Ml))^(1//2)`

Answer

C

Explanation

Consider one of the blocks if the frequency of revolution is f, the angular velocity is `omega=2pif`. The acceleration towards the centre is
`(v^(2))/(l)=omega^(2)l=4pi^(2)f^(2)l`.
The only only horizontal force on the block is the tension of the rod. at the point of breaking, this force is `T_(0)`, so, from newton's laws.
`T_(0)=M*4pi^(2)*f^(2)l`
or `f=(1)/(2pi)((T_(@))/(Ml))^(1//2)`