SATHEE: Properties Of Solids And Liquids Question 234

Properties Of Solids And Liquids Question 234

Question: A large tank is filled with water to a height H. A small hole is made at the base of the tank. It takes $T_{1}$ time to decrease the height of water to $\frac{H}{η} (η > 1)$ ; and it takes $T_{2}$ time to take out the rest of water. If $T_{1} = T_{2}$ , then the value of $η$ is

Options:

A) $\sqrt{\frac{2 h}{g}}$

B) $\sqrt{\frac{2 h}{g} . \frac{D}{d}}$

C) $\sqrt{\frac{2 h}{g} . \frac{d}{D}}$

D) $\sqrt{\frac{2 h}{g}} (\frac{d}{D - d})$

Show Answer

Answer:

Correct Answer: D

Solution:

Upthrust ? weight of body = apparent weight $V D g - V d g = V d a,$

Where a = retardation of body \ $a = (\frac{D - d}{d}) g$

The velocity gained after fall from h height in air, $v = \sqrt{2 g h}$

Hence, time to come in rest, $t = \frac{v}{a} = \frac{\sqrt{2 g h} \times d}{(D - d) g} = \sqrt{\frac{2 h}{g}} \times \frac{d}{(D - d)}$

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Properties Of Solids And Liquids Question 234

Question: A large tank is filled with water to a height H. A small hole is made at the base of the tank. It takes T1 time to decrease the height of water to Hη(η>1) ; and it takes T2 time to take out the rest of water. If T1=T2 , then the value of η is

Options:

Answer:

Solution:

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Question: A large tank is filled with water to a height H. A small hole is made at the base of the tank. It takes $T_{1}$ time to decrease the height of water to $\frac{H}{η} (η > 1)$ ; and it takes $T_{2}$ time to take out the rest of water. If $T_{1} = T_{2}$ , then the value of $η$ is