Solid and Fluids

Practice Questions:

Question 41: moderate

A tank is filled to a height H. The range of water coming out of a hole which is a depth H/4 from the surface of water level is :

1. \[\frac{2H}{\sqrt{3}}\]

2. \[\frac{\sqrt{3}H}{2}\]

3. \[\sqrt{3}H\]

4. \[\frac{3H}{4}\]

View Answer

The horizontal range of water emerging from a hole is given by the formula

$R = 2\sqrt{h(H - h)}$

R = 2\sqrt{\left(\frac{H}{4}\right)\left(\frac{3H}{4}\right)} = 2\left(\frac{\sqrt{3}H}{4}\right) = \frac{\sqrt{3}H}{2}

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Question 42: easy

Two objects A & B of equal density and radius rA = 1 mm and rB = 2 mm are moving in same medium then find the ratio of their terminal velocity $ \frac{v_{B}}{v_{A}}$ in the medium.

1. 1/4

2. 1/2

3. 4

4. 2

View Answer

The terminal velocity $v$ of a spherical object moving through a viscous medium is directly proportional to the square of its radius, expressed as $v \propto r^2$

$v \propto r^2$ , when the density and the medium remain constant.

$\frac{v_B}{v_A} = \left(\frac{r_B}{r_A}\right)^2 = \left(\frac{2}{1}\right)^2 = 4$

Thus, the required ratio \( $\frac{v_B}{v_A}$ is 4 (Option 3).

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