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A solid sphere of density eta (gt 1) tim...

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

A

`((eta-1)/(eta))mg`

B

`eta mg`

C

`(mg)/(eta-1)`

D

`(eta-1)mg`

Text Solution

Verified by Experts

The correct Answer is:
D
`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`
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