Two thin rods of same length `l` but of different uniform mass per unit length `mu_(1)` and `mu_(2)` respectively are joined together. The system is rotated on smooth horizontal plane as shown in figure. The tension at the joint will be

Options

A. A. `3/2 mu_(2)l^(2)omega^(2)`
B. B. `3/2(mu_(1)+mu_(2))l^(2)omega^(2)`
C. C. `3/2 mu_(1)l^(2)omega^(2)`
D. D. `1/2mu_(1)l^(2)omega^(2)`

Answer

A

Explanation

The tension at joint is due to force exerted by the root of linear density `mu_(2)`.
So `F=int_(l)^(2l) mu_(2) dxomega^(2)x=(3mu_(2) omega^(2)l^(2))/2`