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

Tension in spring `T` = upthrust - weight of sphere
`V sigma g - V eta rho g -V rho g` (As `sigma = eta rho)`
`=(eta -1) V rho g =(n-1) mg`.