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. `((alpha -1)/(alpha))mg`
B. `alpha mg`
C. `(mg)/(alpha -1)`
D. `(alpha - 1) mg`

Answer

D

Explanation

Density of sphere `sigma = (rho_omega)/(alpha)`
`(rho_(omega))/(sigma) = alpha`
`F_B = mg + T`
`T = F_B - mg = rho_omega V g - mg`
`rho_omega (m)/(sigma) g - mg`
`((rho_omega)/(sigma) -1) mg = (alpha -1)mg`.
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