Properties Of Matter Ques 54
- 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) $d _A+d _B=2 d _F$
Show Answer
Answer:
Correct Answer: 54.(a,b,d)
Solution:
Formula:
- $F=$ Upthrust $=V d _F g$
Equilibrium of $A$,
$ V d _F g=T+W _A=T+V d _A g $ $\quad$ …….(i)
Equilibrium of $B$,
$ T+V d _F g=V d _B g $ $\quad$ …….(ii)
Adding Eqs. (i) and (ii), we get
$ 2 d _f=d _A+d _B $
$\therefore$ Option (d) is correct
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).
BETA
