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:

  1. $F=$ 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).



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