A hollow sphere of mass M and radius r is immersed in a tank of water (denstiy `rho_(w)`). The sphere would float if it were set free. The sphere is tied to the bottom of the tank by two wires which makes angle `45^(@)` with the horizontal as shown in the figure. The tension `T_(1)` in the wire is :

Options

A. `((4)/(3)piR^(3)rho_(w)g-Mg)/(sqrt(2))`
B. `(2)/(3)piR^(3)rho_(w)g-Mg`
C. `((4)/(3)piR^(3)rho_(w)g-Mg)/(2)`
D. `(4)/(3)piR^(3)rho_(w)g+Mg`

Answer

A

Explanation

`2Tsin45^(@)=B-W`
`2Txx(1)/(sqrt(2))=(4)/(3)piR^(3)rho_(w)g-Mg" "impliesT=((4)/(3)piR^(3)rho_(w)g-Mg)/(sqrt(2))`