 # Mechanical Properties of Fluids Problems

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## Multiple Choice Questions

Question 1
A bowl of soup rests on a table in the dining car of a Rajdhani train. The acceleration of the train is g/4 in the forward direction.
What angle does the surface of the soap make with the horizontal?
(a) ${tan}^{-1} \frac {1}{4}$
(b) ${tan}^{-1}{4}$
(c) ${cos}^{-1}{4}$
(d) ${sin}^{-1}{4}$

## Match the column

Question 2
A block of ice is floating in a liquid of relative density k contained in a beaker
When the ice melts completely, match the column
Column I (k values)
(A) k > 1
(B) k < 1
(C) k=1

Column II
(P) Liquid level will increase
(Q) Liquid level will decrease
(R) Liquid level will remain unchanged
(S) No appropriate match given

## Linked Type comprehensions

(A)A body of density ρ1 is dropped from rest at a height h into a lake of density ρ221)
Neglect all the dissipative effects
Question 3
Calculate the acceleration of this body while it is in the lake
(a) $g(\frac{\rho_2}{\rho_1}-1)$ Upward direction
(b) $g(\frac{\rho_2}{\rho_1}-1)$ Downward direction
(c) $g(1-\frac{\rho_1}{\rho_2})$ Upward direction
(d) $g(1-\frac{\rho_1}{\rho_2})$ Downward direction

Question 4
The maximum depth to which the body sinks before returning to float on the surface is proportional to the height h
And it is given by
H=kh.
What is the value of k
(a)$\frac{\rho_1}{\rho_2-\rho_1}$
(b)$\frac{\rho_2}{\rho_2-\rho_1}$
(c)$\frac{\rho_1}{\rho_2+\rho_1}$
(d) None of these

(B)Water stands at a depth h behind the vertical face of a dam. It exerts a resultant horizontal force on the dam, tending to slide it along its foundation and a torque tending to overturn the dam about the point X. The width of the dam is L.
The density of the water is ρ Question 5
The resulting horizontal force acting on the dam due to water column
(a) Proportional to h2
(b) Proportional to density ρ
(c) Proportional to L
(d) None of these

Question 6 The torque of the forces about point X is given by
(a) $\frac{\rho gl h^3}{3}$
(b) $\frac{\rho g l^2h^3}{6}$
(c) $\frac{\rho gl h^3}{2}$
(d) $\frac{\rho gl h^3}{6}$

## Multiple Choice Questions

Question 7
A piston of Weight W has the form of circular disk with radius R1 . The disk has a hole into which a thin walled pipe with a radius R2 is inserted. The piston can enter a cylinder tightly and without friction and it is initially at the bottom of the cylinder. M kg of water is poured into the pipe. Find the height of the piston above the bottom
(a) $H=\frac{1}{\pi R_1^2\rho}\left[M+\frac{W}{g}\frac{R_2^2}{R_1^2-R_2^2}\right]$
(b) $H=\frac{1}{\pi R_1^2\rho}\left[W-M\frac{R_2^2}{R_1^2-R_2^2}\right]$
(c) $H=\frac{1}{\pi R_1^2\rho}\left[M-\frac{W}{g}\frac{R_1^2}{R_1^2-R_2^2}\right]$
(d) $H=\frac{1}{\pi R_1^2\rho}\left[M-\frac{W}{g}\frac{R_2^2}{R_1^2-R_2^2}\right]$

Question 8
A tank contains water on top of mercury. A cube of iron .06 m along each edge is sitting upright in equilibrium in the liquid.
Density of iron =7.7X103 kg/m3
Density of mercury = 13.6X103 kg/m3
Which one of the following is true
(a) x=32mm and y=28mm
(b) The pressure difference (p2-p1) is 4632 N/m2
(c) The weight of the mercury cube is 16.632 g
(d) None of these

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