# Elasticity and Fluid Machanics-04- Objective Unsolved Level1.pdf

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OBJECTIVE UNSOLVED LEVEL – I 1. As a bubble comes from the bottom of a lake to the top, its radius : (a) Increases (b) Decreases (c) Does not change (d) Becomes zero. 2. An inverted (bell) lying at the bottom of a lake 47.6 m deep has 50 cm3 of air trapped in it. The bell is brought to the surface of the lake. The volume of the trapped air will be (atmospheric pressure = 70 cm of Hg and density of Hg = 13.6 g/cm3). (a) (b) (c) (d) . 3. A hydrogen balloon released on the moon would : (a) Climb up with an acc. of (b) Climb up with an acc. of (c) Neither climb nor fall (d) Fall with an acc. of . 4. A boy carries a fish in one hand and a bucket of water in the other hand; if he places the fish in the bucket, the weight now carried by him : (a) is less than before (b) is more than before (c) is the same as before (d) depends upon his speed. 5. An iceberg is floating partially immersed in sea water. If the density of sea water is and that of ice is , the fraction of the total volume of iceberg above the level of sea water is : (a) 8% (b) 11% (c) 34% (d) 89%. 6. To get the maximum flight, a ball must be thrown as : (a) (b) (c) (d) any of (a), (b) and (c). 7. A sphere of radius r and density  is sinking in container filled with liquid of density  and viscosity . Container is placed in a elevator moving upward with an acceleration . Then terminal velocity of sphere relative to elevator is (a) (b) (c) (d) 8. An L-shaped glass tube is just immersed in flowing water such that its opening is pointing against flowing water. If the speed of water current is , then : (a) The water in the tube rises to height (b) The water in the tube rises to height (c) The water in the tube does not rise at all (d) None of these. 9. A container having a hole at the bottom is free to move on a horizontal surface. As the liquid comes out, the container moves in backward direction with an acceleration and finally acquires a velocity (when all the liquid has drained out). Neglect the mass of container. The correct option out of the following is : (a) Only depends on (b) Only depends on (c) Both and depend on (d) Neither nor depends on . 10. A tube filled with water of density and closed at both ends uniformly rotates in a horizontal plane about a vertical axis. The monometers fixed in the tube at distances and from the axis indicate pressure and respectively. The angular velocity of rotation of the tube will be: (a) (b) (c) (d) . 11. A rod A of weight W is hanging from ceiling. Extension in the rod due to its own weight is . Another identical rod B but negligible mass is also hanging from ceiling. A force of magnitude equal to W is acted on the free end of the rod. The extension in the rod B is . Then is equal to (a) (b) 2 (c) 3 (d) 12. A uniform metal wire fixed at one end is gradually stretched a little beyond its elastic limit-and the

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### Elasticity and Fluid Machanics-04- Objective Unsolved Level1.pdf

• 1. O OB BJ JE EC CT TI IV VE E U UN NS SO OL LV VE ED D L LE EV VE EL L – – I I 1. As a bubble comes from the bottom of a lake to the top, its radius : (a) Increases (b) Decreases (c) Does not change (d) Becomes zero. 2. An inverted (bell) lying at the bottom of a lake 47.6 m deep has 50 cm3 of air trapped in it. The bell is brought to the surface of the lake. The volume of the trapped air will be (atmospheric pressure = 70 cm of Hg and density of Hg = 13.6 g/cm3 ). (a) 3 350cm (b) 3 300cm (c) 3 250cm (d) 3 22cm . 3. A hydrogen balloon released on the moon would : (a) Climb up with an acc. of 2 98 /sec m (b) Climb up with an acc. of 2 98 6 /sec m  (c) Neither climb nor fall (d) Fall with an acc. of 2 (9.8/ 6) /sec m . 4. A boy carries a fish in one hand and a bucket of water in the other hand; if he places the fish in the bucket, the weight now carried by him : (a) is less than before (b) is more than before (c) is the same as before (d) depends upon his speed. 5. An iceberg is floating partially immersed in sea water. If the density of sea water is 1.03 / g cc and that of ice is0.92 / g cc , the fraction of the total volume of iceberg above the level of sea water is : (a) 8% (b) 11% (c) 34% (d) 89%. 6. To get the maximum flight, a ball must be thrown as : (a) v (b) (c) (d) any of (a), (b) and (c). 7. A sphere of radius r and density  is sinking in container filled with liquid of density  and viscosity . Container is placed in a elevator moving upward with an acceleration 2 g . Then terminal velocity of sphere relative to elevator is (a) 2 2 3 9 2 r g           (b)   2 2 9 r g     (c) 2 3 ( ) 2 2 9 g r           (d) 2 1 ( ) 2 2 9 g r          
• 2. 8. An L-shaped glass tube is just immersed in flowing water such that its opening is pointing against flowing water. If the speed of water current is , then : (a) The water in the tube rises to height 2 2g  (b) The water in the tube rises to height 2 2 g  (c) The water in the tube does not rise at all (d) None of these. v h 9. A container having a hole at the bottom is free to move on a horizontal surface. As the liquid comes out, the container moves in backward direction with an acceleration  and finally acquires a velocity  (when all the liquid has drained out). Neglect the mass of container. The correct option out of the following is : (a) Only v depends on h (b) Only  depends on h (c) Both v and  depend on h (d) Neither v nor  depends on h. 10. A tube filled with water of density  and closed at both ends uniformly rotates in a horizontal plane about a vertical axis. The monometers fixed in the tube at distances 1 r and 2 r from the axis indicate pressure 1 p and 2 p respectively. The angular velocity  of rotation of the tube will be: (a) 2 1 2 2 2 1 ( ) 2 ( ) p p r r      (b) 2 1 2 2 2 1 ( ) 2 ( ) p p r r      (c) 2 1 2 2 2 1 2 p p r r     (d) 2 1 2 1 2 p p r r           . r1 r2  P1 P2 11. A rod A of weight W is hanging from ceiling. Extension in the rod due to its own weight is 1 l  . Another identical rod B but negligible mass is also hanging from ceiling. A force of magnitude equal to W is acted on the free end of the rod. The extension in the rod B is 2 l  . Then 1 2 / l l   is equal to (a) 1 3 (b) 2 (c) 3 (d) 1 2 12. A uniform metal wire fixed at one end is gradually stretched a little beyond its elastic limit-and then stretching force is removed. It will (a) remain stretched and will not contract (b) lose its elastic property completely (c) contract, but its final length will be greater than its initial length (d) contract upto the proportional limit. 13. A uniform rod of length  and density  is being pulled on a smooth horizontal floor with an acceleration ‘ a ’. The stress at the transverse cross-section at the mid point of the rod has the magnitude (a) 1 a 2   (b) a   (c) 1 a 4   (d) 3 a 4   .
• 3. 14. The length of a uniform metal wire is observed to be 1  and 2  under the stretching forces 1 F and 2 F . The natural length of the wire is (a) 1 2   (b) 1 2 2    (c) 1 2 2 1 2 1 F F F F     (d) 1 2 2 1 1 2 F F F F     . 15. A large drop of oil (density 3 0.8g/cm and viscosity 0  ) floats up through a column of another liquid (density 3 1.2g/cm and viscosity L  ). Assuming that the two liquids do not mix, the velocity with which the oil drop rises will depend on (a) 0  only (b) L  only (c) both on 0  and L  (d) neither 0  nor L  .
• 4. O OB BJ JE EC CT TI IV VE E U UN NS SO OL LV VE ED D L LE EV VE EL L – – I II I 1. The diagram shows the change x in the length of a thin uniform wire caused by the application of stress F at two different temperatures 1 T and 2 T . The variations shown suggest that : (a) 1 2 T T  (b) 1 2 T T  (c) 1 2 T T  (d) None of these. T2 F x T1 2. A wire can be broken by applying a load of 20 kg wt. The force required to break the wire of twice the diameter is : (a) 20 kg wt (b) 5 kg wt (c) 80 kg wt (d) 160 kg wt. 3. One end of a uniform wire of length L and of weight W is attached rigidly to a point in the roof and a weight 1 W is suspended from its lower end. If S is the area of cross-section of the wire, the stress in the wire at a height (3 L /4) from its lower end is : (a) 1 / W S (b) 1 [ ( / 4)]/ W W S  (c) 1 [ (3 / 4)]/ W W S  (d) 1 ( )/ W W S  . 4. A tensile force of 5 2 10  dyne doubles the length of a rubber cord of cross-sectional area 2 2 cm . The Young’s modulus of rubber is : (a) 5 2 4 10 dyne/ cm  (b) 5 2 1 10 dyne/ cm  (c) 5 2 2 10 dyne/ cm  (d) 4 2 1 10 dyne/ cm  . 5. Two rods of different materials having coefficients of thermal expansion 1  and 2  and Young’s moduli 1 Y and 2 Y respectively are fixed between two rigid massive walls. The rods are heated such that they undergo the same increase in temperature. There is no bending of the rods. If 1  and 2  are in the ratio 2:3, the thermal stresses developed in the two rods are equal provided 1 2 : Y Y is equal to : (a) 2:3 (b) 1:1 (c) 3:2 (d) 4:9. 6. A uniform rod of massm , length L , area of cross-section A and is rotated about an axis passing through one of its ends and perpendicular to its length with constant angular velocity  in a horizontal plane. If Y the Young’s modulus of the material of rod, the increase in its length due to rotation of rod is : (a) 2 2 m L AY  (b) 2 2 2 m L AY  (c) 2 2 3 m L AY  (d) 2 2 2m L AY  . 7. A ball of mass ‘m’ and radius ‘r’ is released in viscous liquid. The value of its terminal velocity is proportional to : (a) (1/ ) r only (b) / m r (c) 1/ 2 ( / ) m r (d) m only.
• 5. 8. A small spherical solid ball is dropped in a viscous liquid. Its journey in the liquid is best described in the figure shown by : (a) Curve A (b) Curve B (c) Curve C (d) Curve D. A B C D Distance Vel ocity 9. A small spherical solid ball is dropped from a height in a viscous liquid. At the time of entering into liquid, ball’s velocity is greater than terminal velocity. Its journey in the liquid is best described in the figure. (a) Curve A (b) Curve B (c) Curve C (d) Curve D. A B C D t V 10. 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 4 y from the top. When the tank is completely filled with water, the quantities of water flowing out per second from both holes are the same. Then R is equal to : (a) 2 L  (b) 2 L  (c) L (d) 2 L  . 11. A spherical liquid drop of radius R is divided into eight equal droplets. If surface tension isT , then work done in the process will be : (a) 2 2 R T  (b) 2 3 R T  (c) 2 4 R T  (d) 2 2 RT  . 12. An air bubble of radius r in water is at a depth h below the water surface at some instant. If P is atmospheric pressure and d and T are the density and surface tension of water respectively, the pressure inside the bubble will be : (a) (4 / ) P hdg T r   (b) (2 / ) P hdg T r   (c) (2 / ) P hdg T r   (d) (4 / ) P hdg T r   . 13. One end of a uniform capillary tube of inner radius 1.0mm is held vertically such that one end is just dipped in water (surface tension 0.07 N/m  ) and a length of 1cm is outside water. Which of the following option is true? (a) the liquid will keep on overflowing from the open end as the tube length is insufficient (b) the liquid will rise upto the top and will assume flat surface (c) the liquid will rise the full exposed length and the radius of its meniscus will be equal to the radius of the capillary ( 1.0mm  ) (d) the liquid will rise the full length of the tube and will assume a meniscus of radius 1.4 mm  . 14. A vertical glass capillary tube of radius r open at both ends contains some water (surface tension T and density  ). If L be the length of the water column, then (a) 4T L r g   (b) 2T L r g   L
• 6. (c) T L 4r g   (d) T L 2r g   . 15. A uniform rod of mass m , length L , area of cross-section A and Young’s modulus Y hangs from a rigid support. Its elongation under its own weight will be (a) zero (b) mgL/2YA (c) mgL/YA (d) 2mgL/YA .
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