A solid sphere of density `eta (gt 1)` times lighter than water is suspended in a water tank by a string tied to its base as shown in fig. If the mass of the sphere is `m`, then the tension in the string is given by

Options

A. `((eta-1)/(eta))mg`
B. `eta mg`
C. `(mg)/(eta-1)`
D. `(eta-1)mg`

Answer

D

Explanation

`eta rho_s = rho_w`
Tension (T) = upthrust - weight of sphere
`=V rho_w g-V rho_s g implies V eta rho_s g-V rho_s g`
`implies (eta-1)V rho_s g implies (eta-1)m g`