JEE > DC Pandey Solutions for JEE Physics > Fluid Mechanics JEE Advance - Physics, Solution by DC Pandey

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Page 1 For JEE Advanced Assertion and Reason Directions : Choose the correct option. (a) If both Assertion and Reason are true and the Reason is correct explanation of the Assertion. (b) If both Assertion and Reason are true but Reason is not the correct explanation of Assertion. (c) If Assertion is true, but the Reason is false. (d) If Assertion is false but the Reason is true. Q 1. Assertion: Pressure is a vector quantity. Reason : Pressure F P A ? . Here F, the force is a vector quantity. Q 2. Assertion : Surface tension F T l ?? ? ?? ?? is not a vector quantity. Reason : Direction of force is specified. Q 3. Assertion : At depth 'h' below the water surface pressure is P. Then at depth '2A' pressure will be 2P. (Ignore density variation). Reason : With depth pressure increases linearly. Q 4. Assertion: Weight of solid in air is W and in water is 2W 3 . Then relative density of solid is 3.0. Reason : Relative density of any solid is given by : Weight in air RD Change in weight in water ? Q 5. Assertion : Water is filled in a U-tube of different cross-sectional area on two sides as shown in figure. Now equal amount of oil (RD = 0.5) is poured on two sides. Level of water on both sides will remain unchanged. Reason : Same weight of oil poured on two sides will produce different pressures. Q 6. Assertion : An ideal fluid is flowing through a pipe. Speed of fluid particles is more at places where pressure is low. Reason : Bernoulli's theorem can be derived from work-energy theorem. Q 7. Assertion : In the figure shown v and R will increase if pressures above the liquid surface inside the chamber is increased. Reason : Value of v or R is independent of density of liquid. Page 2 For JEE Advanced Assertion and Reason Directions : Choose the correct option. (a) If both Assertion and Reason are true and the Reason is correct explanation of the Assertion. (b) If both Assertion and Reason are true but Reason is not the correct explanation of Assertion. (c) If Assertion is true, but the Reason is false. (d) If Assertion is false but the Reason is true. Q 1. Assertion: Pressure is a vector quantity. Reason : Pressure F P A ? . Here F, the force is a vector quantity. Q 2. Assertion : Surface tension F T l ?? ? ?? ?? is not a vector quantity. Reason : Direction of force is specified. Q 3. Assertion : At depth 'h' below the water surface pressure is P. Then at depth '2A' pressure will be 2P. (Ignore density variation). Reason : With depth pressure increases linearly. Q 4. Assertion: Weight of solid in air is W and in water is 2W 3 . Then relative density of solid is 3.0. Reason : Relative density of any solid is given by : Weight in air RD Change in weight in water ? Q 5. Assertion : Water is filled in a U-tube of different cross-sectional area on two sides as shown in figure. Now equal amount of oil (RD = 0.5) is poured on two sides. Level of water on both sides will remain unchanged. Reason : Same weight of oil poured on two sides will produce different pressures. Q 6. Assertion : An ideal fluid is flowing through a pipe. Speed of fluid particles is more at places where pressure is low. Reason : Bernoulli's theorem can be derived from work-energy theorem. Q 7. Assertion : In the figure shown v and R will increase if pressures above the liquid surface inside the chamber is increased. Reason : Value of v or R is independent of density of liquid. Q 8. Assertion : A ball is dropped from a certain height above the free surface of an ideal fluid. When the ball enters the liquid it may accelerate or retard. Reason : Ball accelerates or retards it all depends on the density of ball and the density of liquid. Q 9. Assertion : On moon barometer height will be six times compared to the height or earth. Reason : Value of 'g' on moon's surface is 1 6 the value of 'g' on earth's surface. Q 10. Assertion : In the siphon shown in figure, pressure at P is equal to atmospheric pressure. Reason : Pressure at Q is atmospheric pressure and points P and Q are at same levels. Q 11. Assertion : Force of buoyancy due to atmosphere on a small body is almost zero (or negligible). Reason : If a body is completely submerged in a fluid, then buoyant force is zero. Answers 1. (d) 2. (a) 3. (d) 4. (a) 5. (d) 6. (d) 7. (b) 8. (a) 9. (d) 10. (d) 11. (c) Solutions 1. The magnitude of normal force per unit area is defined as pressure and so it is scalar quantity, not a vector, so assertion is false. 2. Assertion and reason are true with correct explanation. 3. Assertion is false as p(h) = p0 + h ?g while p(2h) = p0 + 2h ?y i.e., p(2h) ? 2p(h) 4. V ? g = W while, ? ? = 3 ?. Assertion is true and reason is correct explanation as Page 3 For JEE Advanced Assertion and Reason Directions : Choose the correct option. (a) If both Assertion and Reason are true and the Reason is correct explanation of the Assertion. (b) If both Assertion and Reason are true but Reason is not the correct explanation of Assertion. (c) If Assertion is true, but the Reason is false. (d) If Assertion is false but the Reason is true. Q 1. Assertion: Pressure is a vector quantity. Reason : Pressure F P A ? . Here F, the force is a vector quantity. Q 2. Assertion : Surface tension F T l ?? ? ?? ?? is not a vector quantity. Reason : Direction of force is specified. Q 3. Assertion : At depth 'h' below the water surface pressure is P. Then at depth '2A' pressure will be 2P. (Ignore density variation). Reason : With depth pressure increases linearly. Q 4. Assertion: Weight of solid in air is W and in water is 2W 3 . Then relative density of solid is 3.0. Reason : Relative density of any solid is given by : Weight in air RD Change in weight in water ? Q 5. Assertion : Water is filled in a U-tube of different cross-sectional area on two sides as shown in figure. Now equal amount of oil (RD = 0.5) is poured on two sides. Level of water on both sides will remain unchanged. Reason : Same weight of oil poured on two sides will produce different pressures. Q 6. Assertion : An ideal fluid is flowing through a pipe. Speed of fluid particles is more at places where pressure is low. Reason : Bernoulli's theorem can be derived from work-energy theorem. Q 7. Assertion : In the figure shown v and R will increase if pressures above the liquid surface inside the chamber is increased. Reason : Value of v or R is independent of density of liquid. Q 8. Assertion : A ball is dropped from a certain height above the free surface of an ideal fluid. When the ball enters the liquid it may accelerate or retard. Reason : Ball accelerates or retards it all depends on the density of ball and the density of liquid. Q 9. Assertion : On moon barometer height will be six times compared to the height or earth. Reason : Value of 'g' on moon's surface is 1 6 the value of 'g' on earth's surface. Q 10. Assertion : In the siphon shown in figure, pressure at P is equal to atmospheric pressure. Reason : Pressure at Q is atmospheric pressure and points P and Q are at same levels. Q 11. Assertion : Force of buoyancy due to atmosphere on a small body is almost zero (or negligible). Reason : If a body is completely submerged in a fluid, then buoyant force is zero. Answers 1. (d) 2. (a) 3. (d) 4. (a) 5. (d) 6. (d) 7. (b) 8. (a) 9. (d) 10. (d) 11. (c) Solutions 1. The magnitude of normal force per unit area is defined as pressure and so it is scalar quantity, not a vector, so assertion is false. 2. Assertion and reason are true with correct explanation. 3. Assertion is false as p(h) = p0 + h ?g while p(2h) = p0 + 2h ?y i.e., p(2h) ? 2p(h) 4. V ? g = W while, ? ? = 3 ?. Assertion is true and reason is correct explanation as 5. Assertion is false as due to different cross-sectional area and height of oil columns will be different producing different pressures which lead to different water levels in the limbs of U-tube. 6. Assertion is not always true as it also depends upon the height from ground. 7. Assertion and reason are both true but not correct explanation as v depends upon P while R depends upon v. 8. Assertion is true and reason is correct explanation as acceleration or retardation depends upon force of buoyancy which in turn depends upon densities of ball and liquid. 9. Assertion is false as barometer measures air pressure but on moon, there is no atmosphere to exert pressure, the barometer reading will be zero. 10. At P, liquid is in motion such that at that point pressure is less than atmospheric pressure. So, assertion is false. 11. Assertion and reason are both false as force of buoyancy can be negligible only when relative density of the body in very high in comparison to that of air, it is not true. Objective Questions Single Correct Option Q 1. A cubical open vessel of side 5 m filled with a liquid is accelerated with an acceleration a. The value of a so that pressure at mid point of A C is equal to atmospheric pressure is (a) g (b) 2g (c) g/2 (d) 2g/5 Q 2. An ice cube is floating in water above which a layer of lighter oil is poured. As the ice melts completely, the level of interface and the upper most level of oil will respectively (a) rise and fall (b) fall and rise (c) not change and no change (d) not change and fall Q 3. An open vessel full of water is falling freely under gravity. There is a small hole in one face of the vessel as shown in the figure. The water which comes out from the hole at the instant when hole is at height H above the ground, strikes the ground at a distance of x from P. Which of the following is correct for the situation described? Page 4 For JEE Advanced Assertion and Reason Directions : Choose the correct option. (a) If both Assertion and Reason are true and the Reason is correct explanation of the Assertion. (b) If both Assertion and Reason are true but Reason is not the correct explanation of Assertion. (c) If Assertion is true, but the Reason is false. (d) If Assertion is false but the Reason is true. Q 1. Assertion: Pressure is a vector quantity. Reason : Pressure F P A ? . Here F, the force is a vector quantity. Q 2. Assertion : Surface tension F T l ?? ? ?? ?? is not a vector quantity. Reason : Direction of force is specified. Q 3. Assertion : At depth 'h' below the water surface pressure is P. Then at depth '2A' pressure will be 2P. (Ignore density variation). Reason : With depth pressure increases linearly. Q 4. Assertion: Weight of solid in air is W and in water is 2W 3 . Then relative density of solid is 3.0. Reason : Relative density of any solid is given by : Weight in air RD Change in weight in water ? Q 5. Assertion : Water is filled in a U-tube of different cross-sectional area on two sides as shown in figure. Now equal amount of oil (RD = 0.5) is poured on two sides. Level of water on both sides will remain unchanged. Reason : Same weight of oil poured on two sides will produce different pressures. Q 6. Assertion : An ideal fluid is flowing through a pipe. Speed of fluid particles is more at places where pressure is low. Reason : Bernoulli's theorem can be derived from work-energy theorem. Q 7. Assertion : In the figure shown v and R will increase if pressures above the liquid surface inside the chamber is increased. Reason : Value of v or R is independent of density of liquid. Q 8. Assertion : A ball is dropped from a certain height above the free surface of an ideal fluid. When the ball enters the liquid it may accelerate or retard. Reason : Ball accelerates or retards it all depends on the density of ball and the density of liquid. Q 9. Assertion : On moon barometer height will be six times compared to the height or earth. Reason : Value of 'g' on moon's surface is 1 6 the value of 'g' on earth's surface. Q 10. Assertion : In the siphon shown in figure, pressure at P is equal to atmospheric pressure. Reason : Pressure at Q is atmospheric pressure and points P and Q are at same levels. Q 11. Assertion : Force of buoyancy due to atmosphere on a small body is almost zero (or negligible). Reason : If a body is completely submerged in a fluid, then buoyant force is zero. Answers 1. (d) 2. (a) 3. (d) 4. (a) 5. (d) 6. (d) 7. (b) 8. (a) 9. (d) 10. (d) 11. (c) Solutions 1. The magnitude of normal force per unit area is defined as pressure and so it is scalar quantity, not a vector, so assertion is false. 2. Assertion and reason are true with correct explanation. 3. Assertion is false as p(h) = p0 + h ?g while p(2h) = p0 + 2h ?y i.e., p(2h) ? 2p(h) 4. V ? g = W while, ? ? = 3 ?. Assertion is true and reason is correct explanation as 5. Assertion is false as due to different cross-sectional area and height of oil columns will be different producing different pressures which lead to different water levels in the limbs of U-tube. 6. Assertion is not always true as it also depends upon the height from ground. 7. Assertion and reason are both true but not correct explanation as v depends upon P while R depends upon v. 8. Assertion is true and reason is correct explanation as acceleration or retardation depends upon force of buoyancy which in turn depends upon densities of ball and liquid. 9. Assertion is false as barometer measures air pressure but on moon, there is no atmosphere to exert pressure, the barometer reading will be zero. 10. At P, liquid is in motion such that at that point pressure is less than atmospheric pressure. So, assertion is false. 11. Assertion and reason are both false as force of buoyancy can be negligible only when relative density of the body in very high in comparison to that of air, it is not true. Objective Questions Single Correct Option Q 1. A cubical open vessel of side 5 m filled with a liquid is accelerated with an acceleration a. The value of a so that pressure at mid point of A C is equal to atmospheric pressure is (a) g (b) 2g (c) g/2 (d) 2g/5 Q 2. An ice cube is floating in water above which a layer of lighter oil is poured. As the ice melts completely, the level of interface and the upper most level of oil will respectively (a) rise and fall (b) fall and rise (c) not change and no change (d) not change and fall Q 3. An open vessel full of water is falling freely under gravity. There is a small hole in one face of the vessel as shown in the figure. The water which comes out from the hole at the instant when hole is at height H above the ground, strikes the ground at a distance of x from P. Which of the following is correct for the situation described? (a) The value of x is 2hH 2 3 (b) The value of x is 4hH 3 (c) The value of x can't be computed from information provided (d) The question is irrevalent as no water comes out from the hole Q 4. A uniform rod AB, 12 m long weighing 24 kg, is supported at end B by a flexible light string and a lead weight (of very small size) of 12 kg attached at end A. The rod floats in water with one-half of its length submerged. For this situation, mark out the correct statement. [Take g = 10 m/s 2 , density of water = 1000 kg/m 3 ] (a) The tension in the string is 36 g (b) The tension in the string is 12 g (c) The volume of the rod is 6.4 × 10 -2 m 3 (d) The point of application of the buoyancy force is passing through C (centre of mass of rod) Q 5. A water hose pipe of cross-section area 5 cm 2 is used to fill a tank of 120 L. It has been observed that it takes 2 min to fill the tank. Now, a nozzle with an opening of cross-section area 1cm 2 is attached to the hose. The nozzle is held so that water is projected horizontally from a point 1 m above the ground. The horizontal distance over which the water can be projected is (Take g = 10m/s 2 ) (a) 3 m (b) 8 m (c) 4.47 m (d) 8.64 m Q 6. The height of water in a vessel is h. The vessel wall of width h is at an angle ? to the vertical. The net force exerted by the water on the wall is (a) 1 3 ? bh 2 g cos ? (b) 1 2 ? h 2 ?g (c) 1 2 ? bh 2 g sec ? (d) zero Q 7. A body of density ? is dropped from rest from a height h into a lake of density ?( ? > ?). The maximum depth the body sinks inside the liquid is (neglect viscous effect of liquid) Page 5 For JEE Advanced Assertion and Reason Directions : Choose the correct option. (a) If both Assertion and Reason are true and the Reason is correct explanation of the Assertion. (b) If both Assertion and Reason are true but Reason is not the correct explanation of Assertion. (c) If Assertion is true, but the Reason is false. (d) If Assertion is false but the Reason is true. Q 1. Assertion: Pressure is a vector quantity. Reason : Pressure F P A ? . Here F, the force is a vector quantity. Q 2. Assertion : Surface tension F T l ?? ? ?? ?? is not a vector quantity. Reason : Direction of force is specified. Q 3. Assertion : At depth 'h' below the water surface pressure is P. Then at depth '2A' pressure will be 2P. (Ignore density variation). Reason : With depth pressure increases linearly. Q 4. Assertion: Weight of solid in air is W and in water is 2W 3 . Then relative density of solid is 3.0. Reason : Relative density of any solid is given by : Weight in air RD Change in weight in water ? Q 5. Assertion : Water is filled in a U-tube of different cross-sectional area on two sides as shown in figure. Now equal amount of oil (RD = 0.5) is poured on two sides. Level of water on both sides will remain unchanged. Reason : Same weight of oil poured on two sides will produce different pressures. Q 6. Assertion : An ideal fluid is flowing through a pipe. Speed of fluid particles is more at places where pressure is low. Reason : Bernoulli's theorem can be derived from work-energy theorem. Q 7. Assertion : In the figure shown v and R will increase if pressures above the liquid surface inside the chamber is increased. Reason : Value of v or R is independent of density of liquid. Q 8. Assertion : A ball is dropped from a certain height above the free surface of an ideal fluid. When the ball enters the liquid it may accelerate or retard. Reason : Ball accelerates or retards it all depends on the density of ball and the density of liquid. Q 9. Assertion : On moon barometer height will be six times compared to the height or earth. Reason : Value of 'g' on moon's surface is 1 6 the value of 'g' on earth's surface. Q 10. Assertion : In the siphon shown in figure, pressure at P is equal to atmospheric pressure. Reason : Pressure at Q is atmospheric pressure and points P and Q are at same levels. Q 11. Assertion : Force of buoyancy due to atmosphere on a small body is almost zero (or negligible). Reason : If a body is completely submerged in a fluid, then buoyant force is zero. Answers 1. (d) 2. (a) 3. (d) 4. (a) 5. (d) 6. (d) 7. (b) 8. (a) 9. (d) 10. (d) 11. (c) Solutions 1. The magnitude of normal force per unit area is defined as pressure and so it is scalar quantity, not a vector, so assertion is false. 2. Assertion and reason are true with correct explanation. 3. Assertion is false as p(h) = p0 + h ?g while p(2h) = p0 + 2h ?y i.e., p(2h) ? 2p(h) 4. V ? g = W while, ? ? = 3 ?. Assertion is true and reason is correct explanation as 5. Assertion is false as due to different cross-sectional area and height of oil columns will be different producing different pressures which lead to different water levels in the limbs of U-tube. 6. Assertion is not always true as it also depends upon the height from ground. 7. Assertion and reason are both true but not correct explanation as v depends upon P while R depends upon v. 8. Assertion is true and reason is correct explanation as acceleration or retardation depends upon force of buoyancy which in turn depends upon densities of ball and liquid. 9. Assertion is false as barometer measures air pressure but on moon, there is no atmosphere to exert pressure, the barometer reading will be zero. 10. At P, liquid is in motion such that at that point pressure is less than atmospheric pressure. So, assertion is false. 11. Assertion and reason are both false as force of buoyancy can be negligible only when relative density of the body in very high in comparison to that of air, it is not true. Objective Questions Single Correct Option Q 1. A cubical open vessel of side 5 m filled with a liquid is accelerated with an acceleration a. The value of a so that pressure at mid point of A C is equal to atmospheric pressure is (a) g (b) 2g (c) g/2 (d) 2g/5 Q 2. An ice cube is floating in water above which a layer of lighter oil is poured. As the ice melts completely, the level of interface and the upper most level of oil will respectively (a) rise and fall (b) fall and rise (c) not change and no change (d) not change and fall Q 3. An open vessel full of water is falling freely under gravity. There is a small hole in one face of the vessel as shown in the figure. The water which comes out from the hole at the instant when hole is at height H above the ground, strikes the ground at a distance of x from P. Which of the following is correct for the situation described? (a) The value of x is 2hH 2 3 (b) The value of x is 4hH 3 (c) The value of x can't be computed from information provided (d) The question is irrevalent as no water comes out from the hole Q 4. A uniform rod AB, 12 m long weighing 24 kg, is supported at end B by a flexible light string and a lead weight (of very small size) of 12 kg attached at end A. The rod floats in water with one-half of its length submerged. For this situation, mark out the correct statement. [Take g = 10 m/s 2 , density of water = 1000 kg/m 3 ] (a) The tension in the string is 36 g (b) The tension in the string is 12 g (c) The volume of the rod is 6.4 × 10 -2 m 3 (d) The point of application of the buoyancy force is passing through C (centre of mass of rod) Q 5. A water hose pipe of cross-section area 5 cm 2 is used to fill a tank of 120 L. It has been observed that it takes 2 min to fill the tank. Now, a nozzle with an opening of cross-section area 1cm 2 is attached to the hose. The nozzle is held so that water is projected horizontally from a point 1 m above the ground. The horizontal distance over which the water can be projected is (Take g = 10m/s 2 ) (a) 3 m (b) 8 m (c) 4.47 m (d) 8.64 m Q 6. The height of water in a vessel is h. The vessel wall of width h is at an angle ? to the vertical. The net force exerted by the water on the wall is (a) 1 3 ? bh 2 g cos ? (b) 1 2 ? h 2 ?g (c) 1 2 ? bh 2 g sec ? (d) zero Q 7. A body of density ? is dropped from rest from a height h into a lake of density ?( ? > ?). The maximum depth the body sinks inside the liquid is (neglect viscous effect of liquid) (a) h ? ? ? ? (b) h ? ? ? ? (c) h ? ? (d) h ? ? Q 8. A liquid stands at the plane level in the U-tube when at rest. If areas of cross-section of both the limbs are equal, what will be the difference in heights h of the liquid in the two limbs of U-tube, when the system is given an acceleration a in horizontal direction towards right as shown? (a) 2 gL aH (b) La g (c) 2 La Hg (d) Lg a Q 9. A liquid of density ? and surface tension ? rises in a capillary tube of inner radius R. The angle of contact between the liquid and the glass is ?. The point A lies just below the meniscus in the tube and the point B lies at the outside level of liquid in the beaker as shown in figure. The pressure at A is (a) pB - ?gh (b) B 2 cos p R ?? ? (c) atm 2 cos p R ?? ? (d) All of these Q 10. A large open tank has two holes in the wall. One is a square hole of side L at a depth h from the top and the other is a circular hole of radius R at a depth 4h from the top. When the tank is completely filled with water, quantities of water flowing out per second from both holes are the same. Then R is equal to (a) L 2 ? (b) 2 ?L (c) L (d) L 2 ? Q 11. Two identical cylindrical vessels with their bases at the same level each contain a liquid of density ?. The area of either base is A but in one vessel the liquid height is h1 and in the other liquid height is h2 (h2 < h1). If the two vessels are connected, the work done by gravity in equalizing the levels is (a) 2 12 1 (h h ) A g 2 ?? (b) 12 1 (h h )A g 2 ?? (c) 22 12 1 (h h )A g 2 ?? (d) 2 12 1 (h h ) A g 4 ?? Q 12. A cubical block of side 10 cm floats at the interface of an oil and water as shown in the figure. The density of oil is 0.6 g cm -3 and the lower face of ice cube is 2 cm below the interface. The pressure above that of the atmosphere at the lower face of the block isRead More

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