Practice Questions

Q6. A bob of mass m attached to an inextensible string of length l is suspended from a vertical support. The bob rotates in a horizontal circle with an angular speed ω rad/s about the vertical. About the point of suspension : (1) Angular momentum is conserved (2) Angular momentum changes in magnitude but not in direction (3) Angular momentum changes in direction but not (4) Angular momentum changes both in direction and in magnitude magnitude

Q7. Four particles, each of mass M and equidistant from each other, move along a circle of radius R under the action of their mutual gravitational attraction. The speed of each particle is JEE Main 2014 (06 Apr) JEE Main Previous Year Paper (1) √GMR (2) √2√2 GMR + + R (1 R (1 2√2) (3) √GM (4) 1 2√2) 2 √GM

Q7. The bulk moduli of ethanol, mercury and water are given as 0.9, 25 and 2.2 respectively in units of 109Nm−2 . For a given value of pressure, the fractional compression in volume is ΔV . Which of the following statements V about ΔVV for these three liquids is correct ? (1) Ethanol > Water > Mercury (2) Water > Ethanol > Mercury (3) Mercury > Ethanol > Water (4) Ethanol > Mercury > Water

Q7. The gravitational field in a region is given by →g= (5ˆi 12ˆj) energy of a particle of mass 2 kg when it is taken from the origin to a point (7 m, −3 m) is (1) 71 J (2) 13√58 J (3) 2 J (4) 1 J

Q8. A capillary tube is immersed vertically in water and the height of the water column is x. When this arrangement is taken into a mine of depth d, the height of the water column is y. If R is the radius of earth, the ratio xy is : (1) ( RR +− dd ) (2) ( RR +− dd ) (3) (1 −2dR ) (4) (1 −dR )

Q8. Steel ruptures when a shear of 3.5 × 108 N m−2 is applied. The force needed to punch a 1 cm diameter hole in a steel sheet 0.3 cm thick is nearly: (1) 1.4 × 104 N (2) 2.7 × 104 N (3) 3.3 × 104 N (4) 1.1 × 104 N

Q8. The average mass of rain drops is 3.0 × 10−5 kg and their avarage terminal velocity is 9 m/s. Calculate the energy transferred by rain to each square metre of the surface at a place which receives 100 cm of rain in a year. (1) 3.5 × 105 J (2) 4.05 × 104 J (3) 3.0 × 105 J (4) 9.0 × 104 J

Q8. The velocity of water in a river is 18 km h−1 near the surface. If the river is 5 m deep, find the shearing stress between the horizontal layers of water. The coefficient of viscosity of water = 10−2 poise. (1) 10−4 N m−2 (2) 10−3 N m−2 (3) 10−2 N m−2 (4) 10−1 N m−2

Q8. There is a circular tube in a vertical plane. Two liquids which do not mix and of densities d1 and d2 are filled in the tube. Each liquid subtends 90o angle at centre. Radius joining their interface makes an angle α with vertical. Ratio d1 is : d2 (1) 1+sinα (2) 1+cosα 1−sinα 1−cosα (3) 1+tanα (4) 1+sinα 1−tanα 1−cosα

Q9. On heating water, bubbles being formed at the bottom of the vessel detatch and rise. Take the bubbles to be spheres of radius R and making a circular contact of radius r with the bottom of the vessel. If r << R, and the surface tension of water is T, value of r just before bubbles detatch is : (density of water is ρw ) (1) R2√2ρw3T g ​ (2) R2√ρw6Tg (3) R2√ρwT g (4) R2√3ρwT g

Q9. Water of volume 2 L in a closed container is heated with a coil of 1 kW. While water is heated, the container loses energy at a rate of 160 J/s. In how much time will the temperature of water rise from 27oC to 77oC ? (Specific heat of water is 4.2 kJ/kg and that of the container is negligible). (1) 8 min 20 s (2) 7 min (3) 14 min (4) 6 min 2 s

Q9. A tank with a small hole at the bottom has been filled with water and kerosene (specific gravity 0.8 ). The height of water is 3 m and that of kerosene 2 m. When the hole is opened the velocity of fluid coming out from it is nearly: (take g = 10 ms−2 and density of water = 103 kg m−3) (1) 10.7 ms−1 (2) 9.6 ms−1 (3) 8.5 ms−1 (4) 7.6 ms−1

Q9. A cylindrical vessel of cross-section A contains water to a height h. There is a hole in the bottom of radius ' a '. The time in which it will be emptied is: (1) 2 A (2) √2 A πa2 √hg πa2 √hg (3) 2√2 A (4) A g πa2 √h g √2πa2 √h

Q9. A large number of liquid drops each of radius r coalesce to form a single drop of the radius R. The energy released in the process is converted into kinetic energy of the big drop so formed. The speed of the big drop is (given surface tension of the liquid T , density ρ ) ( 1r −1R ) (1) √2Tρ ( 1r −1R ) (2) √6Tρ ( 1r −1R ) (3) √4Tρ ( 1r −1R ) (4) √Tρ

Q10.An air bubble of radius 0.1 cm is in a liquid having surface tension 0.06 N/m and density 103 kg/m3 . The pressure inside the bubble is 1100Nm−2 greater than the atmospheric pressure. At what depth is the bubble below the surface of the liquid? (g = 9.8 ms−2) (1) 0.1 m (2) 0.15 m (3) 0.20 m (4) 0.25 m

Q10.An open glass tube is immersed in mercury in such a way that a length of 8 cm extends above the mercury level. The open end of the tube is then closed and sealed and the tube is raised vertically up by additional 46 cm. What will be length of the air column above mercury in the tube now ? (Atmospheric pressure = 76 cm of Hg) (1) 16 cm (2) 22 cm (3) 38 cm (4) 6 cm

Q10.The equation of state for a gas is given by PV = nRT + αV , where n is the number of moles and α is a positive constant. The initial temperature and pressure of one mole of the gas contained in a cylinder are T0 and P0 respectively. The work done by the gas when its temperature doubles isobarically will be : (1) P0 T0 ln 2 (2) P0T0RP0+α (3) P0T0R (4) P0 T0R P0−α

Q10.Two soap bubbles coalesce to form a single bubble. If V is the subsequent change in volume of contained air and S change in total surface area, T is the surface tension and P atmospheric pressure, then which of the following relation is correct? (1) 4PV + 3ST = 0 (2) 3PV + 4ST = 0 (3) 2PV + 3ST = 0 (4) 3PV + 2ST = 0

Q10. In the diagram shown, the difference in the two tubes of the manometer is 5 cm, the cross-section of the tube at A and B is 6 mm2 and 10 mm2 respectively. The rate at which water flows through the tube is (g = 10 m s−2) JEE Main 2014 (19 Apr Online) JEE Main Previous Year Paper (1) 7. 5 cc s−1 (2) 12. 5 cc s−1 (3) 8. 0 cc s−1 (4) 10. 0 cc s−1

Q11.The pressure that has to be applied to the ends of a steel wire of length 10 cm to keep its length constant when its temperature is raised by 100 °C is : (For steel, Young's modulus is 2 × 1011 N m−2 and coefficient of thermal expansion is 1. 1 × 10−5 K−1 ) (1) 2 .2 ×108 Pa (2) 2 .2 ×109 Pa (3) 2 .2 ×107 Pa (4) 2 .2 ×106 Pa

Q11.Hot water cools from 60∘C to 50∘C in the first 10 minutes and to 42∘C in the next 10 minutes. The temperature of the surroundings is: (1) 25∘C (2) 10∘C (3) 15∘C (4) 20∘C

Q11.Modern vacuum pumps can evacuate a vessel down to a pressure of 4.0 × 10−15 atm. at room temperature (300 K). Taking R = 8.3 JK-1 mole-1, 1 atm = 105 Pa and NAvogadro = 6 × 1023 mole−1 , the mean distance between molecules of gas in an evacuated vessel will be of the order of : (1) 0. 2 μm (2) 0. 2 mm (3) 0. 2 cm (4) 0. 2 nm JEE Main 2014 (09 Apr Online) JEE Main Previous Year Paper

Q11.A hot body, obeying Newton's law of cooling is cooling down from its peak value 80∘C to an ambient temperature of 30∘C. It takes 5 minutes in cooling down from 80∘C to 40∘C. How much time will it take to cool down from 62∘C to 32∘C ? (Given In 2 = 0.693, In 5 = 1.609 ) (1) 3.75 minutes (2) 8.6 minutes (3) 9.6 minutes (4) 6.5 minutes

Q11.A black coloured solid sphere of radius R and mass M is inside a cavity with a vacuum inside. The walls of the cavity are maintained at temperature T0 . The initial temperature of the sphere is 3T0 . If the specific heat of the material of the sphere varies as αT 3 per unit mass with the temperature T of the sphere, where α is a constant, then the time taken for the sphere to cool down to temperature 2T0 will be ( σ is Stefan Boltzmann constant) (1) 16πR2σ Mα ln( 32 ) (2) 16πR2σMα ln( 163 ) (3) 4πR2σ Mα ln( 23 ) (4) 4πR2σMα ln( 163 )

Q12.A Carnot engine absorbs 1000 J of heat energy from a reservoir at 127∘C and rejects 600 J of heat energy during each cycle. The efficiency of engine and temperature of sink will be: JEE Main 2014 (12 Apr Online) JEE Main Previous Year Paper (1) 20% and −43∘C (2) 40% and −33∘C (3) 50% and −20∘C (4) 70% and −10∘C