Properties of Matter 2 Question 15
15. Two solid spheres $A$ and $B$ of equal volumes but of different densities $d _A$ and $d _B$ are connected by a string. They are fully immersed in a fluid of density $d _F$. They get arranged into an equilibrium state as shown in the figure with a tension in the string. The arrangement is possible only if
(2011)
(a) $d _A<d _F$
(b) $d _B>d _F$
(c) $d _A>d _F$
(d) $d _A+d _B=2 d _F$
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Answer:
Correct Answer: 15. (a, b, d)
Solution:
- $F=$ Upthrust $=V d _F g$
Equilibrium of $A$,
$$ V d _F g=T+W _A=T+V d _A g \cdots(i) $$
Equilibrium of $B$,
$$ T+V d _F g=V d _B g \cdots(ii) $$
Adding Eqs. (i) and (ii), we get
$\therefore$ Option (d) is correct
$$ 2 d _f=d _A+d _B $$
From Eq. (i) we can see that $d _F>d _A \quad($ as $T>0)$
$\therefore$ Option (a) is correct.
From Eq. (ii) we can see that, $d _B>d _F$
$\therefore$ Option (b) is correct.
$\therefore$ Correct options are (a), (b) and (d).
