Pascal's Law

Q. The three vessels shown in figure have same base area. Equal volumes of a liquid are poured into the three vessels. The force on the base will be

1. Maximum in vessel $A$
2. Maximum in vessel $B$
3. Maximum in vessel $C$
4. Equal in all the vessels

Q. If pressure at half depth of a lake is equal to $\frac{2}{3}rd$ pressure at the bottom of the lake, then what is the depth of the lake?
(Take atmospheric pressure as ${10}^5\text{Pa}$, density of water as $1000{\text{kg/m}}^3$ and $g=10{\text{m/s}}^2$)

1. $6.67\text{m}$
2. $60\text{m}$
3. $20\text{m}$
4. $10\text{m}$

Q.

A hydraulic automobile lift is designed to lift cars with a maximum mass of 3000 kg. The area of cross-section of the piston carrying the load is $425c{m}^2$ . What maximum pressure would the smaller piston have to bear?

Q. In a car lift, compressed air exerts a force $F_1$ on a small piston having a radius of $5.0\text{cm}$. This pressure is transmitted to the second piston of radius $10.0\text{cm}$. If the mass of the car to be lifted by the second piston is $1350\text{kg}$, calculate $F_1$ [Take $g=10{\text{m/s}}^2$]

1. $1800\text{N}$
2. $3375\text{N}$
3. $5625\text{N}$
4. $2400\text{N}$

Q.

What are the methods of measuring surface tension?

Q. The pressure at the bottom of a tank of water is $3P$ where $P$ is the atmospheric pressure. If the water is drawn out till the level of water is lowered by one-fifth, the pressure at the bottom of the tank will now be:

1. $\frac{8}{5}P$
2. $\frac{4}{5}P$
3. $2P$
4. $\frac{13}{5}P$

Q. In a hydraulic jack as shown, mass of the car is $W=800\text{kg},A_1=10{\text{cm}}^2,A_2=10{\text{m}}^2$. The minimum force $F$ required to lift the car is: [Take $g=10{\text{m/s}}^2$]

1. $1\text{N}$
2. $0.8\text{N}$
3. $8\text{N}$
4. $16\text{N}$

Q. A uniformly tapering vessel is filled with a liquid of density $900{\text{kg/m}}^3$. The force that acts on the base of the vessel due to the liquid (excluding atmospheric force) is : [Take $g=10{\text{m/s}}^2$]

1. $3.6\text{N}$
2. $7.2\text{N}$
3. $9.0\text{N}$
4. $12.6\text{N}$

Q.

A stone of mass 2kg is tied to a string of length 0.5m. If the breaking tension of the string is 900N, then the maximum angular velocity, the stone can have in uniform circular motion is:

1. 20 rad/s

2. 10 rad/s

3. 40 rad/s

4. 30 rad/s

Q.

What are the three steps of scientific method?

Q. An air bubble of radius $1\text{cm}$ in water has an upward acceleration $9.8{\text{cm/s}}^2.$ The density of water is $1{\text{g/cm}}^3$ and water offers negligible drag force on the bubble. The mass of the bubble is $(g=980{\text{cm/s}}^2)$

1. $\text{4.51 gm}$
2. $\text{3.15 gm}$
3. $\text{4.15 gm}$
4. $\text{1.52 gm}$

Q. A piston of cross-sectional area $100{\text{cm}}^2$ is used in a hydraulic pump to exert a force of ${10}^7\text{dyne}$ on the water. The cross-sectional area of the other piston which supports a truck of mass $2000\text{kg}$ is

1. $9.8\times {10}^2{\text{cm}}^2$
2. $9.8\times {10}^3{\text{cm}}^2$
3. $1.96\times {10}^3{\text{cm}}^2$
4. $1.96\times {10}^4{\text{cm}}^2$

Q. Consider a solid sphere of radius $R$ and mass density $\rho \left(r\right)={\rho }_0(1-\frac{r^2}{R^2}),0<r\le R$. The minimum density of a liquid in which it will float is:

1. $\frac{{\rho }_0}{3}$
2. $\frac{{\rho }_0}{5}$
3. $\frac{2{\rho }_0}{5}$
4. $\frac{2{\rho }_0}{3}$

Q.

What is the dimensional formula of pressure difference?

Q. There is a circular tube in a vertical plane. Two liquids which do not mix and of densities $d_1$ and $d_2$ are filled in the tube. Each liquid subtends ${90}^{\circ }$ angle at centre. Radius joining their interface makes an angle $\alpha$ with vertical.
Ratio $\frac{d_1}{d_2}$ is:

1. $\frac{1+\text{tan}\alpha }{1-\text{tan}\alpha }$
2. $\frac{1+\text{sin}\alpha }{1-\text{cos}\alpha }$
3. $\frac{1+\text{sin}\alpha }{1-\text{sin}\alpha }$
4. $\frac{1+\text{cos}\alpha }{1-\text{cos}\alpha }$

Q. To lift an automobile of $5000\text{kg}$, a hydraulic lift with a large piston $800{\text{cm}}^2$ in area is employed. Calculate the force that must be applied to a small piston of area $5{\text{cm}}^2$ to achieve it.

1. $612.5\text{N}$
2. $306.25\text{N}$
3. $153.12\text{N}$
4. $408.56\text{N}$

Q. Find the depth of a lake( in $\text{km}$ ) at which the density of water is $1\%$ greater than at the surface, if compressibility of water is $50\times {10}^{-6}/\text{atm}$

Q.

$Newton-meter$ is the SI unit of

1. Thrust

2. Pressure

3. Torque

4. Work

Q. In a hydraulic lift, compressed air exerts a force $F_1$ on a small piston having a radius of $5\text{cm}$. This pressure is transmitted to a second piston of radius $15\text{cm}$. If the mass of the load to be lifted is $1350\text{kg}$, calculate the pressure acting on the smaller piston.
[Take $g=10{\text{m/s}}^2$]

1. $3\times {10}^5\text{Pa}$
2. $2\times {10}^5\text{Pa}$
3. $1.9\text{Pa}$
4. $1.9\times {10}^5\text{Pa}$

Q. The apparent depth of water in a cylindrical water tank of diameter $2R\text{cm}$ is reducing at the rate of $x\text{cm/min}$ when water is being drained out at a constant rate. The actual amount of water drained in ${\text{cm}}^3\text{/min}$ is
$(n_1=$ refractive index of air, $n_2=$ refractive index of water$)$

1. $\frac{x\pi R^2{n}_1}{n_2}$
2. $\frac{x\pi R^2{n}_2}{n_1}$
3. $\frac{2\pi R{n}_1}{n_2}$
4. $\pi R^{2}x$

Q. The force acting on a window of area $50\text{cm}\times 50\text{cm}$ of a submarine at a depth of $2000\text{m}$ in an ocean, interior of which is maintained at sea level atmospheric pressure is
(Density of sea water $={10}^3{\text{kg/m}}^3,g=10{\text{m/s}}^2$ )

1. ${10}^6\text{N}$
2. $25\times {10}^6\text{N}$
3. $5\times {10}^5\text{N}$
4. $5\times {10}^6\text{N}$

Q.

Find the force exerted by the water on a 2 $m^2$ plane surface of a large stone placed at the bottom of a sea 500 m deep. Does the force depend on the orientation of the surface ?

Q. A tube $1{\text{cm}}^2$ in cross section is attached to the top of a vessel $1\text{cm}$ high and of cross section $100{\text{cm}}^2$. Water is poured into the system filling it upto a height of $100\text{cm}$ above the bottom of the vessel as shown in the figure. Take $g=10{\text{m/s}}^2$. Find the correct statement. Take atmospheric pressure $P_0={10}^5\text{bar}$.

1. The weight of water in the system is $1.99\text{N}$.
2. Both (a) and (b) are correct.
3. Neither (a) nor (b) is correct.
4. The force exerted by the water against the bottom of the vessel is $1100\text{N}$.

Q.

The action of paint gun is based on:

Q.

A steel blade float on the surface of pure water when detergent is added, it sinks.why?

Q.

Kerosene oil rises up in the wick of a lantern because of:

1. The gravitational pull of the wick

2. Buoyant force of air

3. Surface tension

4. Diffusion of the oil through the wick

Q. A plate of mass 10 gm is in equilibrium in air due to the force exerted by light beam on plate. Calculate power of the beam. Assume plate is perfectly absorbing.

1. $3\times {10}^{7}W$
2. $2\times {10}^{7}W$
3. $3\times {10}^{5}W$
4. $2\times {10}^{5}W$

Q. A hydraulic automobile lift is designed to lift cars with a maximum mass of $300\text{kg}$. The area of cross-section of the piston carrying the load is $500{\text{cm}}^2$. What maximum pressure would smaller piston have to bear?

1. ${5.88\times 10}^4\text{Pa}$
2. ${8.55\times 10}^4\text{Pa}$
3. ${2.94\times 10}^4\text{Pa}$
4. ${11.66\times 10}^4\text{Pa}$

Q.

A cylindrical tank of height 0.4 m is open at the top and has a diameter of 0.16 m. It is filled with water upto a height of 0.16 m. Find the time taken to empty the tank through a hole of radius 5 x 10^-3 m in its bottom.

1. t = 23.5 s

2. t = 47.3 s

3. t = 19.02 s

4. t = 46.26 s

Q.

Consider the situation in figure. The bottom of the pot is a reflecting plane mirror, S is a small fish and T is human eye. Refractive index of water is $\mu$.

(a) At what distance(s) from itself will the fish see the image(s) of the eye ?

(b) At what distance(s) from itself will the eye see the image(s) of the fish.