SATHEE: Properties of Matter 2 Question 15

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) $d_{B} > d_{F}$

(d) $d_{A} + d_{B} = 2 d_{F}$

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Answer:

Correct Answer: 15. (b, c)

Solution:

$F =$ Upthrust $= V d_{F} g$

Equilibrium of $A$ ,

Equilibrium of $B$ ,

$V d_{F} g = T + W_{A} = T + V d_{A} g$

$T + V d_{F} g = V d_{B} g$

Adding Eqs. (i) and (ii), we get

$∴$ Option (d) is correct

$2 d_{f} = d_{A} + d_{B}$

From Eq. (i) we can see that $d_{F} > d_{A} ($ as $T > 0)$

$∴$ Option (a) is correct.

From Eq. (ii) we can see that, $d_{B} > d_{F}$

$∴$ Option (b) is correct.

$∴$ Correct options are (a), (b) and (d).

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Properties of Matter 2 Question 15

15. Two solid spheres A and B of equal volumes but of different densities dA and dB are connected by a string. They are fully immersed in a fluid of density dF. They get arranged into an equilibrium state as shown in the figure with a tension in the string. The

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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