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Fluid Mechanics Physics - Fluid Mechanics

Rajasthan Board (RBSE) - STD 12 Science - Physics (Rajasthan - English Medium). 81 questions in this chapter.

Question types

Fluid Mechanics question types

81 questions across 6 question groups — pick any mix to generate a Physics paper with step-by-step answer keys.

81
Questions
6
Question groups
5
Question types
Sample Questions

Fluid Mechanics questions

One sample from each question group in this chapter. Select any group above to see the full set with answer keys.

Q 1M.C.Q (1 Marks)1 Mark
The weight of an empty balloon on a spring balance is $W_1.$ The weight becomes $W_2$ when the balloon is filled with air. Let the weight of the Air itself be $\omega$ neglect the thickness of the balloon when it is filled with air. Also neglect the difference in the densities of air inside and outside the balloon.
  • A
    $\text{W}_2=\text{W}_1$
  • B
    $\text{W}_2=\text{W}_1+\omega$
  • ✓
    $\text{W}_2 < \text{W}_1+\omega$
  • D
    $\text{W}_2 > \text{W}_1$

Answer: C.

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Q 2M.C.Q (1 Marks)1 Mark
Water and mercury are filled in two cylindrical vessels up to same height. Both vessels have a hole in the wall near the bottom. The velocity of water and mercury coming Out of the holes are $v_1$ and $v_{2 }$ respectively.
  • ✓
    $\text{v}_1=\text{v}_2$
  • B
    $\text{v}_1=13.6\text{v}_2$
  • C
    $\text{v}_1=\frac{\text{v}_2}{\text{13.6}\cdot}$
  • D
    $\text{v}_1=\sqrt{13.6}\text{v}_2$

Answer: A.

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Q 3M.C.Q (1 Marks)1 Mark
Equal mass of three liquids are kept in three identical cylindrical vessels $A, B$ and $C.$ The densities are $P_A, P_B, P_C$ with $P_A < P_B < P_C$ The force on the base will be$:$
  • A
    Maximum in vessel $A.$
  • B
    Maximum in vessel $B.$
  • C
    Maximum in vessel $C.$
  • ✓
    Equal in all the vessels.

Answer: D.

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Q 4M.C.Q (1 Marks)1 Mark
Consider the equations $\text{P}=\lim_\limits{\triangle\text{s}\rightarrow0}\frac{\text{F}}{\triangle\text{s}}$ and $\text{P}_1-\text{P}_2-\text{pgz}$ In an elevator accelerating upward.
  • A
    Both the equations are valid.
  • ✓
    The first is valid but not the second.
  • C
    The second is valid but not the first.
  • D
    Both are invalid.

Answer: B.

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Q 5M.C.Q (1 Marks)1 Mark
A large cylindrical tank has a hole of area A at its bottom. Water is poured in the tank by a tube of equal cross-sectional area A ejecting water at the speed v.
  1. The water level in the tank will keep on rising.
  2. No water can be stored in the tank.
  3. The water level will rise to a height $\frac{\text{v}^2}{2\text{g}}$ and then stop.
  4. The water level will oscillate.
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Q 71 Marks Question1 Mark
At Deoprayag (Garhwal, UP) river Alaknanda mixes with the river Bhagirathi and becomes river Ganga. Suppose Alaknanda has a width of 12m, Bhagirathi has a width of 8m and Ganga has a width of 16m. Assume that the depth of water is same in the three rivers. Let the average speed of water in Alaknanda be 20km/h and in Bhagirathi be 16km/h. Find the average speed of water in the river Ganga.
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Q 81 Marks Question1 Mark
Solve the previous problem if the lead piece is fastened on the top surface of the block and the block is to float with its upper surface just dipping into water.
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Q 91 Marks Question1 Mark
A cubical block of wood weighing 200g has a lead piece fastened underneath. Find the mass of the lead piece which will just allow the block to float in water. Specific gravity of wood is 0.8 and that of lead is 11.3.
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Q 101 Marks Question1 Mark
A cubical block of ice floating in water has to support a metal piece weighing $0.5\ kg.$ What can be the minimum edge of the block so that it does not sink in water? Specific gravity of ice $= 0^9.$
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Q 112 Marks Questions2 Marks
A cube of ice floats partly in water and partly in $K.$ oil Find the ratio of the volume of ice immersed in water to that in $K.$ oil. Specific gravity of $K$. oil is $0.8$ and that of ice is $0.9$.
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Q 132 Marks Questions2 Marks
Suppose the tube in the previous problem is kept vertical with $A$ upward but the other conditions remain the same. The separation between the cross$-$sections at $A$ and $B$ is $\frac{15}{16}\text{cm}.$ Repeat parts $(a), (b)$ and $(c)$ of the previous problem. Take $g = 10\ m/s^2.$
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Q 142 Marks Questions2 Marks
A $U-$ tube containing a liquid is accelerated horizontally with a constant acceleration $a_0.$ If the separation between the vertical limbs is $1,$ find the difference in the heights of the liquid in the two arms.
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Q 152 Marks Questions2 Marks
Water flows through a horizontal tube of variable cross$-$section. The area of cross-section at $A$ and $B$ are $4\ mm^2$ and $2\ mm^2$ respectively. If $1cc$ of water enters per second through $A,$ find,
  1. The speed ofwater at $A.$
  2. The speed of water at $B.$
  3. Thepressure difference $P_A- P_{B.}$
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Q 163 Marks Question3 Marks
A cube of ice of edge 4cm is placed in an empty cylindrical glass of inner diameter 6cm. Assume that the ice melts uniformly from each side so that it always retains its cubical shape. Remembering that ice is lighter than water, find the length of the edge of the ice cube at the instant it just leaves contact with the bottom of the glass.
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Q 173 Marks Question3 Marks
A cylindrical object of outer diameter $10\ cm,$ height $20\ cm$ and density $8000\ kg/m^3$ is supported by a vertical spring and is half dipped in water as shown in.
  1. Find the elongation of the spring in equilibrium condition.
  2. If the object is slightly depressed and released, find the time period of resulting oscillations of the object. The spring constant $= 500N/m.$
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Q 183 Marks Question3 Marks
A glass full of water has a bottom of area $20\ cm^2,$ top of area $20\ cm^2,$ height $20\ cm$ and volume half a litre.
  1. Find the force exerted by the water on the bottom.
  2. Considering the equilibrium of the water, find the.
Resultant force exerted by the sides of the glass on the water. Atmospheric pressure $ = 1.0 \times 10^5N/m^2.$ Density of water $= 1000\ kg/m^3$ and $g = 10m/s^2$. Take all numbers to be exact.
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Q 193 Marks Question3 Marks
Water is filled in a rectangular tank of size $3m \times 2m \times 1m.$
  1. Find the total force exerted by the water on the bottom surface of the tank.
  2. Consider a vertical side of area $2m \times 1m.$ Take a horizontal strip of width $ox$ metre in this side, situated at a depth of $x$ metre from the surface of water. Find the force by the water on this strip.
  3. Find the torque of the force calculated in part.$(b)$ about the bottom edge of this side.
  4. Find the total force by the water on this side.
  5. Find the total torque by the water on the side about.
The bottom edge. Neglect the atmospheric pressure and take $g = 10m/s^2.$
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Q 203 Marks Question3 Marks
Suppose the glass of the previous problem is covered by a jar and the air inside the jar is completely pumped out.
  1. What will be the answers to the problem?
  2. Show that the answers do not change if a glass of different shape is used provided the height, the bottom area and the volume are unchanged.
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Q 214 Marks Questions4 Marks
In the derivation of $P_1 - P_2 = Pgz,$ it was assumed that the liquid is incompressible. Why will this equation not be strictly valid for a compressible liquid?
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Q 224 Marks Questions4 Marks
Suppose the density of air at Madras is $P_0$ and atomospheric pressure is $P_0.$ If we go up, the density and the pressure both decrease. Suppose we wish to calculate the pressure at a height $10\ km$ above Madras. If we use the equation $P_{0 }- P = pogz,$ will we get a pressure more than the actual or less than the actual? Neglect the variation in $g.$ Does your answer change if you also consider the variation in $g$?
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Q 234 Marks Questions4 Marks
While watering a distant plant, a gardener partially water than in fresh closes the exit hole of the pipe by putting his finger on it. Explain why this results in the water stream goirig to a larger distance.
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Q 244 Marks Questions4 Marks
Refer to the previous problem. Suppose, the goldsmith argues that he has not mixed copper or any other material with gold, rather some cavities might have been left inside the ornament. Calculate the volume of the cavities left that will allow the weights given in that problem.
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Q 255 Marks Questions5 Marks
An ornament weighing $36g$ in air, weighs only $34g$ in water. Assuming that some copper is mixed with gold to prepare the ornament, find the amount of copper in it. Specific gravity of gold is $19.3$ and that of copper is $8.9$.
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Q 265 Marks Questions5 Marks
A cubical metal block of edge 12cm floats in mercury with one fifth of the height inside the mercury. Water is poured till the surface of the block is just immersed in it. Find the height of the water column to be poured. Specific gravity of mercury = 13.6.
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Q 275 Marks Questions5 Marks
Water leaks out from an open tank through a hole of area $2\ mm^2$ in the bottom. Suppose water is filled up to a height of $80\ cm$ and the area of cross $-$ section of the tank is $0.4m^2$. The pressure at the open surface and at the hole are equal to the atmospheric pressure. Neglect the small velocity of the water near the open surface in the tank.
  1. Find the initial speed of water coming out of the hole.
  2. Find the speed of water coming out when half of water has leaked out.
  3. Find the volume of water leaked out during a time interval dt after the height remained is $h$. Thus find the decrease in height dh in terms of $h$ and dt.
  4. From the result of part $c$ find the time required for half of the water to leak out.
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