LEVEL – I

1. A and B are two metallic pieces. They are fully immersed in water and then weighed. Now they show same loss of weight. The conclusion therefore is:

(A) A and B have same weight in air

(B) A and B have equal volumes

(C) The densities of the materials of A and B are the same

(D) A and B are immersed to the same depth inside water.

2. An ice cube contains a large air bubble. The cube is floating on the surface of water contained on a trough. What will happen to the water level, when the cube melts?

(A) It will remain unchanged

(B) It will fall

(C) It will rise

(D) First it will and then rise

3. In a hydraulic lift, used at a service station the radius of the large and small piston are in the ratio of 20 : 1. What weight placed on the small piston will be sufficient to lift a car of mass 1500 kg?

(A) 3.75Kg

(B) 37.5Kg

(C) 7.5Kg

(D) 75Kg

4. Water and mercury are filled in two cylindrical vessels upto 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. Thus

(A) v_{1} = v_{2}

(B) v_{1} = 13.6v_{2}

(C) v_{1} = v_{2}/13.6

(D) v_{1} = √(13.6v_{2})

5. An ice cube contains a glass ball. The cube is floating on the surface of water contained in a trough on the surface of water contained in a trough. What will happen to the water level, when the cube melts?

(A) It will remain unchanged

(B) It will fall

(C) It will rise

(D) First it will fall and then rise

6. A square hole of side length l is made at a depth of y and a circular hole is made at a depth of 4y from the surface of water in a water tank kept on a horizontal surface. If equal amount of water comes out of the vessel through the holes per second then the radius of the circular hole is equal to(r, l << y) :

(A) l / √2

(B) l / 2

(C) l / √π

(D) l / √2π

7. In the figure shown a liquid is flowing through a tube at the rate of 0.1 m^{3}/sec. The tube is branched into two semi circular tubes of cross sectional area A/3 and 2A/3. The velocity of liquid at Q is (the cross-section of the main tube (A) = 10^{-2} m^{2} and V_{P} = 20 m/sec.):

(A) 5 m/sec

(B) 30 m/sec

(C) 35 m/sec

(D) None of these.

8. A small hole is made at a height of h’ = (1/√2 ) m from the bottom of a cylindrical water tank and at a depth of h = √2 m from the upper level of water in the tank. The distance, where the water emerging from the hole strikes the ground is:

(A) 2√2m

(B) 1 m

(C) 2 m

(D) None of these.

9. The excess pressure inside one soap bubble is three time that inside a second soap bubble. The ratio of the volumes of the two bubbles

(A) 1/9

(B) 9/1

(C) 1/27

(D) 27/1

10. An air bubble of diameter 2 mm rises steadily through a solution of density 1750 kg/m^{3} at the rate of .35 cm/sec. Coefficient of viscosity of the solution is (Assume mass of the bubble to be negligible)

(A) 9 poise

(B) 6 poise

(C) 11 poise

(D) 4 poise

__ANSWER:__

1. B 2. A 3. A 4. A 5. B 6. C 7. D 8. D 9 C 10. A

LEVEL – I

11. The velocity of the water flowing from the inlet pipe is less than the velocity of water flowing out from the spin pipe B.

(A) variation of water level in vessel will be irregular.

(B) water level will remains constant.

(C) the water level will perform periodic oscillation motions.

(D) none of the above.

12. In a streamline flow of a liquid

(A) every particle has its own velocity, different from others.

(B) all particles move with a constant velocity, even if the path is curvilinear.

(C) At a point on the streamline, particle can have two velocities.

(D) At a point on the streamline, particle can have only one velocity along the tangent.

13. A metallic sphere floats in an immiscible mixture of water (ρ_{w} = 10^{3} kg/m^{3}) and a liquid (ρ_{L} = 13. 5 × 10^{3} kg/m^{3}) such that 4/5 portion is in water and (1/5)th portion is in the liquid. The density of the metal in kg/m^{3} is

(A) 4.5 × 10^{3}

(B) 4.0 × 10^{3}

(C) 3.5 × 10^{3}

(D) 3.0 × 10^{3}

14. A stream line body with relative density d_{1} falls into air from a height h1 on the surface of a liquid of relative density d_{2} , where d_{2} is greater than d_{1} . The time of immersion of the body into the liquid will be

(A) $ \displaystyle \sqrt{\frac{2 h_1}{g}} \times \frac{d_1}{d_2 – d_1} $

(B) $\displaystyle \sqrt{\frac{2 h_1}{g}} $

(C) $ \displaystyle \sqrt{\frac{2 h_1}{g}} \times \frac{d_1}{d_2 } $

(D) $ \displaystyle \sqrt{\frac{2 h_1}{g}} \times \frac{d_2}{ d_1} $

15. A tank is filled with water to a height H. Two holes are made on its side wall, one at a height of h from the bottom and other at a depth h from the top. The horizontal jets starting from the two holes meet the ground or side (in level with the bottom of the tank) at the same point. This distance of this point from the side of the tank is

(A) $ \displaystyle \sqrt{4 h(H – h)} $

(B) $ \displaystyle \sqrt{ h(H – h)} $

(C) $ \displaystyle \sqrt{2 h(H-h)} $

(D) $ \displaystyle \sqrt{3 h(H-h)} $

16. Which of the following graphs best represents the relation between the height h of the liquid in a capillary tube and radius of the capillary tube?

(A)

(B)

(C)

(D)

17. A boat floating in a tank is carrying passengers. If the passengers drink water, how will it affect the water level of the tank?

(A) It will go down

(B) It will rise

(C) It will remain unchanged

(D)It will depend on atmospheric pressure.

18. A cylinder is filled with non viscous liquid of density d to a height h_{o} and a hole is made at a height h_{1} from the bottom of the cylinder. The velocity of liquid issuing out of the hole is

(A) $ \displaystyle \sqrt{2 g h_o } $

(B) $ \displaystyle \sqrt{2 g (h_o – h_1 )} $

(C) $ \displaystyle \sqrt{d g h_1 } $

(D) $ \displaystyle \sqrt{d g h_o } $

19. A spherical ball of mass m and radius r is allowed to fall in a medium of viscosity η . The time in which the velocity of the body increases from zero to 0.63 times the terminal velocity is called time constant (τ). Dimensionally τ can be represented by

(A) mr^{2}/6πη

(B) $ \displaystyle \sqrt{\frac{6 \pi m r \eta}{g^2}} $

(C) m/6πηr

(D) none of these.

20. A large bottle is fitted with a capillary siphon. Ratio of times taken to empty the bottle when it is filled with (i) water (ii) petroleum of relative density 0.8.

(η_{water} = 0.001 poise, η_{petroleum} = 0.002 poise, d_{water} = 1000 kg/m^{3})

(A) 5/4

(B) 4/5

(C) 2/5

(D) 3/5

__ANSWER:__

11. C 12. D 13. C 14. A 15. A 16. C 17. D 18. D 19. C 20. C