Practice Questions

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 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. 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. 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. 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. 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

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. 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. 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

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. 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

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

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.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.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.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

Q12.During an adiabatic compression, 830 J of work is done on 2 moles of a diatomic ideal gas to reduce its volume by 50%. The change in its temperature is nearly: (R = 8.3JK−1 mol−1) (1) 40 K (2) 33 K (3) 20 K (4) 14 K

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

Q12.A monoatomic gas is compressed from a volume of 2 m3 to a volume of 1 m3 at a constant pressure of 100 N m2 . Then it is heated at constant volume by supplying 150 J of energy. As a result, the internal energy of the gas (1) Decreases by 50 J (2) Increases by 250 J (3) Decreases by 250 J (4) 0 J

Q13.A gas molecule of mass M at the surface of the earth has kinetic energy equivalent to 0 °C. If it were to go up straight without colliding with any other molecules, how high it would rise? Assume that the height attained is much less than the radius of the earth. ( kB is Boltzmann constant) (1) 273kB (2) 819kB 2Mg 2Mg (3) 0 (4) 546kB3Mg

Q13.One mole of diatomic ideal gas undergoes a cyclic process ABC as shown in figure. The process BC is adiabatic. The temperatures at A, B and C are 400 K, 800 K and 600 K respectively. Choose the correct statement : (1) The change in internal energy in whole cyclic (2) The change in internal energy in the process CA process is 250 R is 700 R. (3) The change in internal energy in the process AB (4) The change in internal energy in the process BC is - 350 R is - 500 R

Q13.At room temperature a diatomic gas is found to have an r.m.s. speed of 1930 ms−1 . The gas is: (1) H2 (2) Cl2 (3) O2 (4) F2

Q14.A body is in simple harmonic motion with time period T = 0.5 s and amplitude A = 1 cm. Find the average velocity in the interval in which it moves from equilibrium position to half of its amplitude. (1) 16 cm/s (2) 6 cm/s (3) 4 cm/s (4) 12 cm/s

Q14.A particle which is simultaneously subjected to two perpendicular simple harmonic motions represented by; x = a1 cos ωt and y = a2 cos 2ωt traces a curve given by : JEE Main 2014 (09 Apr Online) JEE Main Previous Year Paper (1) (2) (3) (4)

Q14.The angular frequency of the damped oscillator is given by, ω = √( constant, m is the mass of the oscillator and r is the damping constant. If the ratio mkr2 is 8%, the change in time period compared to the undamped oscillator is approximately as follows: (1) increases by 1% (2) increases by 8% (3) decreases by 1% (4) decreases by 8%