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A solid sphere of density $\eta(\gt1)$ 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
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The correct answer is:
$(\eta-1) m g$
Tension in spring $T=$ upthrust - weight of sphere
$=V \sigma g-V \rho g=V \eta \rho g-V \rho g \quad(\mathrm{~A} s \sigma=\eta \rho)$
$=(\eta-1) V \rho g=(\eta-1) m g$.
$=V \sigma g-V \rho g=V \eta \rho g-V \rho g \quad(\mathrm{~A} s \sigma=\eta \rho)$
$=(\eta-1) V \rho g=(\eta-1) m g$.
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