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9-1.Fluid Mechanics
medium
A solid sphere of density $\eta$ $( > 1)$ 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
$\left( {\frac{{\eta - 1}}{\eta }} \right)\,mg$
B
$\eta mg$
C
$\frac{{mg}}{{\eta - 1}}$
D
$(\eta - 1)\,mg$
Solution
(d)Tension in spring $T =$ upthrust $-$ weight of sphere
$ = V\sigma g – V\rho g$$ = V\eta \rho g – V\rho g$$({\rm{As }}\sigma = \eta \rho )$
$ = (\eta – 1)V\rho g$= $(\eta – 1)mg.$
Standard 11
Physics
