Mechanical Properties of Fluids Test

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Mechanical Properties of Fluids Test - 72

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Question 1
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An ideal liquid of density $$\rho $$ is filled in a horizontally fixed syringe fitted with piston. There is no friction between the piston and the inner surface of the syringe. Cross-section area of the syringe is A An orifice is made at one end of the syringe. When the piston is pushed into the syringe, the liquid comes out of the orifice and then following a parabolic path falls on the ground.
With what velocity does the liquid come out of the orifice?

A
$$\sqrt { \dfrac { F }{ \rho A } } $$

B
$$\sqrt { \dfrac { 2F }{ \rho A } } $$

C
$$\sqrt { \dfrac { F+2\rho ghA }{ \rho A } } $$

D
$$\sqrt { \dfrac { F+\rho ghA }{ \rho A } } $$

Solution
Question 2
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An object of volume $$0.5 m^3$$ and density $$500 kg/m^3$$ is glued to the flat bottom of a vessel containing water. The flat base of the object glued to the bottom has an area $$100 cm^2$$ and density of water is $$1.0 g/cm^3$$. If the maximum force that the glue can withstand is $$2000 N$$, to what maximum height above the base can water be filled in the vessel so that the object is not torn apart from the base?

A
$$5 m$$

B
$$10 m$$

C
Up to any height

D
Insufficient information

Solution
Question 3
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A cylindrical vessel is filled with water to a height $$H$$. A vessel has two small holes in the side, from which water is rushing out horizontally and the two streams strike the ground at the same point. If the lower hole $$Q$$ is $$h$$ height above the ground, then the height of hole $$P$$ above the ground will be

A
$$2h$$

B
$$H/h$$

C
$$H - h$$

D
$$H/2$$

Solution
Question 4
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Directions For Questions

A cylindrical tank having cross-sectional area $$A=0.5m^2$$ is filled with two liquids of density $$\rho_1=900kgm^-3$$ and $$\rho_2=600kgm^-3$$, to a height $$h=60cm$$ each as shown in the figure. A small hole having area $$a=5cm^2$$ is made in right vertical wall at height $$y=20cm$$ from the bottom. A horizontal force $$F$$ is applied on the tank to keep it in static equilibrium. The tank is lying on horizontal surface. neglect mass of the cylindrical tank in comparison to mass of the liquids (take $$g=10ms^-2$$).

...view full instructions

The velocity of efflux is

A
$$10ms^-1$$

B
$$20ms^-1$$

C
$$4ms^-1$$

D
$$35ms^-1$$

Solution

Since area of a hole is very small in comparison to base area. $$A$$ of the cylinder, velocity of liquid inside the cylinder is negligible. Let velocity of efflux be $$v$$ and atmospheric pressure be $$P_0$$.

Consider two points A (inside the cylinder) and B (just outside the hole) in the same horizontal line as shown in the figure in question.
Pressure at $$A, P_A=P_0+h\rho_2g+\left(h-y\right)\rho_1{g}$$
Pressure at $$B$$, $$P_B=P_0$$

According to Bernoulli's theorem,
Pressure energy at $$A=Pressure\ energy\ at\ B+ Kinetic\ energy\ at\ B$$
$$\therefore P_A=P_B+\dfrac{1}{2}\rho_1v^2$$
$$\therefore v=4ms^-1$$
Question 5
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Directions For Questions

A tube of uniform cross section is used to siphon water from a vessel $$V$$ as shown in the figure. The pressure over the open end of water in the vessel is atmospheric pressure $$\left(P_0\right)$$. The heights of the tube above and below the water level in the vessel are $$h_1$$ and $$h_2$$, respectively.

...view full instructions

Determine the velocity $$v_{B}$$ of the water issuing out at B.

A
$$v_B=\sqrt{2gh_{2}}$$

B
$$v_B=\sqrt{2g\left(h_{1}+h_{2}\right)}$$

C
$$v_B=\sqrt{2g\left(h_{2}-h_{1}\right)}$$

D
$$v_B=\sqrt{gh_{2}}$$

Solution

As long as water fills the tube (as shown in the figure) and points $$A$$ and $$B$$ are open to the atmosphere, the velocity at $$B$$ will be given by Torricelli's theorem.
Hence, $$v_B=\sqrt{2gh_2}$$ where $$h_2$$ is the difference in the levels $$A$$ and $$B$$.
Question 6
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A cylinder of mass m and density $$\rho$$ hanging from a string is lowered into a vessel of cross-sectional area s containing a liquid of density $$\sigma (< \rho)$$ until it is fully immersed. The increase in pressure at the bottom of the vessel is?

A
$$\dfrac{m\rho g}{\sigma s}$$

B
$$\dfrac{mg}{s}$$

C
$$\dfrac{m\sigma g}{\rho s}$$

D
Zero

Solution
Question 7
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A bent tube is lowered into water stream as shown in the figure. The velocity of the stream relative to the tube is equal to $$v=2\ m/s$$. The closed upper end of the tube locates at height $$h_0=10\ cm$$ above free surface of water has a small orifice. To what height $$h$$ will the water get spurt ?

A
$$5\ cm$$

B
$$10\ cm$$

C
$$20\ cm$$

D
$$40\ cm$$

Solution
Question 8
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A solid ball of density $$\rho_1$$ and radius $$r$$ falls vertically through a liquid of density $$rho_2$$. Assume that the viscous force acting on the ball is $$F=krv$$, where $$k$$ is a constant and $$v$$ its velocity. What is the terminal velocity of the ball ?

A
$$\dfrac{4\pi gr^2( \rho_1-\rho_2)}{3k}$$

B
$$\dfrac{2\pi r( \rho_1-\rho_2)}{3gk}$$

C
$$\dfrac{2\pi g( \rho_1+\rho_2)}{3gr^2k}$$

D
$$None\ of\ these$$

Solution
Question 9
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The area of cross section of the two vertical arms of a hydraulic press are $$1\ cm^2$$ and $$10\ cm^2$$ respectively. A force of $$10\ N$$ applied, as shown in the figure, to a tight fitting light piston in the thinner arms balances a force $$F$$ applied to the corresponding piston in the thicker arm. Assuming, that the levels of water in both the arms are the same, we can conclude :

A
$$F=100\ N$$

B
$$F=25\ N$$

C
$$F=50\ N$$

D
$$F$$, as applied, cannot keep piston in equilibrium

Solution
Question 10
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A cylindrical vessel filled with water upto a height $$h$$ weight $$w$$ and is resting on a horizontal plane. The side wall of the vessel has a plugged circular hole touching the bottom. The coefficient of friction between the bottom of the vessel and the plane is $$\mu$$. The minimum diameter of the hole so that the vessel just begins to move on the floor after the removal of the plug is :

A
$$\sqrt{\dfrac{\pi \mu w}{\rho h g}}$$

B
$$\sqrt{\dfrac{ \mu w}{2\pi \rho h g}}$$

C
$$\sqrt{\dfrac{ \mu w}{\pi \rho h g}}$$

D
$$\sqrt{\dfrac{ 2\mu w}{\pi \rho h g}}$$

Solution