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7. Water is filled in a cylindrical container to a height of 3m. The ratio of the cross-sectional area of the orifice and the beaker is 0.1.

The square of the speed of the liquid coming out from the orifice is (g = 10 m/s2) (a) 50 m2/s2 (b) 50.5 m2/s2 (c) 51 m2/s2 (d) 52 m2/s2 Answer-a (34)

14. A vessel of area of cross-section A has liquid to a height H. There is a hole at the bottom of vessel having area of cross-section a.

The time taken to decrease the level from H1 to H2 will be (a) (A/a)(2/g)[√H1– √H2] (b) √2gh (c) √2gh( H1– H2) …

13. A block of ice floats on a liquid of density 1.2in a beaker then level of liquid when ice completely melt

(a) Remains same (b) Rises (c) Lowers (d) (a), (b) or (c) Answer-b (24)

12. A uniform rod of density ρ is placed in a wide tank containing a liquid of density

ρ0 (ρ0 > ρ) . The depth of liquid in the tank is half the length of the rod. The rod is in equilibrium, with its lower end resting on the bottom of the tank. In this position the rod …

11. Two communicating vessels contain mercury. The diameter of one vessel is n times larger than the diameter of the other. A column of water of height h is poured into the left vessel. The mercury level will rise in the right-hand vessel (s = relative density of mercury and ρ= density of water) by

(a) (n2h)/[(n+1)2s] (b) h/[(n+1)2s] (c) h/[(n2 +1)s] …

10. There are two identical small holes of area of cross-section a on the opposite sides of a tank containing a liquid of density ρ . The difference in height between the holes is h. Tank is resting on a smooth horizontal surface. Horizontal force which will has to be applied on the tank to keep it in equilibrium is

(a) ghρa (b) (2gh)/(ρa) (c) 2ρagh (d) (ρgh)/a Answer-c (19)

9. A cylinder containing water up to a height of 25 cm has a hole of cross-section

1/4 cm2 in its bottom. It is counterpoised in a balance. What is the initial change in the balancing weight when water begins to flow out (a) Increase of 12.5 gm-wt (b) Increase of 6.25 gm-wt (c) Decrease of 12.5 …

8. A large open tank has two holes in the wall. One is a square hole of side L at a depth y from the top and the other is a circular hole of radius R at a depth 4y from the top. When the tank is completely filled with water the quantities of water flowing out per second from both the holes are the same. Then R is equal to

(a) 2πL (b) L/√2π (c) L …

6. A liquid is kept in a cylindrical vessel which is being rotated about a vertical axis through the centre of the circular base. If the radius of the vessel is r and angular velocity of rotation is ω , then the difference in the heights of the liquid at the centre of the vessel and the edge is

(a) (rω)/(2g) (b) (r2 ω2 )/(2g) (c) √2grω (d) (ω2 /(2gr2 ) Answer-b (32)

5. A body floats in a liquid contained in a beaker. The whole system as shown falls freely under gravity. The upthrust on the body due to the liquid is

(a) Zero (b) Equal to the weight of the liquid displaced (c) Equal to the weight of the body in air (d) Equal to the weight of the immersed position of the body Answer-a (8)

18. Assertion : Machine parts are jammed in winter. Reason : The viscosity of lubricant used in machine parts increase at low temperature.

(a) If both assertion and reason are true and the reason is the correct explanation of the assertion. (b) If both assertion and reason are true but reason is not the correct explanation of the assertion. (c) If assertion is …

13. Assertion : For a floating body to be in stable equilibrium, its centre of buoyancy must be located above the centre of gravity. Reason : The torque produced by the weight of the body and the upthrust will restore body back to its normal position, after the body is disturbed.

11. Assertion : The size of the needle of a syninge controls flow rate better than the thumb pressure exerted by a doctor while administering an injection. Reason : Flow rate is independent of pressure exerted by the thumb of the doctor.

9. Assertion : The velocity of flow of a liquid is smaller when pressure is larger and viceversa. Reason : According to Bernoulli’s theorem, for the stream line flow of an ideal liquid, the total energy per unit mass remains constant.

4. A vessel contains oil

(density = 0.8 gm/cm3) over mercury (density = 13.6 gm/cm3). A homogeneous sphere floats with half of its volume immersed in mercury and the other half in oil. The density of the material of the sphere in gm/cm3 is (a) …

3. A wooden block, with a coin placed on its top, floats in water as shown in fig. the distance l and h are shown there. After some time the coin falls into the water. Then

(a) l decreases and h increases (b) l increases and h decreases (c) Both l and h increase (d) Both l and h decrease Answer-d (119)

2. A homogeneous solid cylinder of length L (L<H/2). Cross-sectional area A/5 is immersed such that it floats with its axis vertical at the liquid-liquid interface with length L/4 in the denser liquid as shown in the fig. The lower density liquid is open to atmosphere having pressure

P0 . Then density D of solid is given by (a) 5d/4 (b) 4d/5 (c) d (d) d/5 Answer-a (7)

1. A U-tube in which the cross-sectional area of the limb on the left is one quarter, the limb on the right contains mercury

(density 13.6 g/cm3). The level of mercury in the narrow limb is at a distance of 36 cm from the upper end of the tube. What will be the rise in the level of mercury in the right limb if …

28. Assertion : Bernoulli’s theorem holds for incompressible, non-viscous fluids.

Reason : The factor v2/2g is called velocity head. (a) If both assertion and reason are true and the reason is the correct explanation of the assertion. (b) If both assertion and reason are true but reason is not …