Practice Questions

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.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.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

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.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.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 )

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

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

Q12.Three rods of Copper, Brass and Steel are welded together to form a Y-shaped structure. Area of cross-section of each rod is 4 cm2 . End of copper rod is maintained at 100°C. Where as ends of brass and steel are kept at JEE Main 2014 (06 Apr) JEE Main Previous Year Paper 0°C. Lengths of the copper, brass and steel rods are 46, 13 and 12 cms respectively. The rods are thermally insulated from surroundings except at ends. Thermal conductivities of copper, brass and steel are 0. 92, 0. 26 and 0. 12 CGS units respectively. Rate of heat flow through copper rod is : (1) 1. 2 Cal /s (2) 2. 4 Cal /s (3) 4. 8 Cal /s (4) 6. 0 Cal /s

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.Two bodies of masses 1 kg and 4 kg are connected to a vertical spring, as shown in the figure. The smaller mass executes simple harmonic motion of angular frequency 25 rad s−1 , and amplitude 1. 6 cm while the bigger mass remains stationary on the ground. The maximum force exerted by the system on the floor is (take g = 10 m s−2 ). (1) 20 N (2) 60 N (3) 40 N (4) 10 N

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.The amplitude of a simple pendulum, oscillating in air with a small spherical bob, decreases from 10 cm to 8 cm in 40 seconds. Assuming that Stokes law is valid, and ratio of the coefficient of viscosity of air to that of carbon dioxide is 1.3, the time in which amplitude of this pendulum will reduce from 10 cm to 5 cm in carbondioxide will be close to (ln 5 = 1.601, ln 2 = 0.693). (1) 231 s (2) 142 s (3) 208 s (4) 161 s

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

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.An ideal monoatomic gas is confined in a cylinder by a spring loaded piston of cross section 8.0 × 10−3 m2 . Initially the gas is at 300 K and occupies a volume of 2.4 × 10−3 m3 and the spring is in its relaxed state as shown in figure. The gas is heated by a small heater until the piston moves out slowly by 0.1 m. The force constant of the spring is 8000 N/m and the atmospheric pressure is 1.0 × 105 N/m2 . The cylinder and the piston are thermally insulated. The piston and the spring are massless and there is no friction between the piston and the cylinder. The final temperature of the gas will be: (Neglect the heat loss through the lead wires JEE Main 2014 (11 Apr Online) JEE Main Previous Year Paper of the heater. The heat capacity of the heater coil is also negligible). (1) 300 K (2) 800 K (3) 500 K (4) 1000 K k r2 k is the spring m − 4 m2 ) where

Q14.A particle moves with simple harmonic motion in a straight line. In first τ s, after starting from rest it travels a distance a, and in next τ s it travels 2a, in same direction, then : (1) Amplitude of motion is 3a (2) Time period of oscillations is 8τ (3) Amplitude of motion is 4a (4) Time period of oscillations is 6τ

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.Which of the following expressions corresponds to simple harmonic motion along a straight line, where x is the displacement and a, b, c are positive constants? (1) a + bx −cx2 (2) bx2 (3) a −bx + cx2 (4) −bx

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%

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)

Q15.The total length of a sonometer wire fixed between two bridges is 110 cm. Now, two more bridges are placed to divide the length of the wire in the ratio 6 : 3 : 2 . If the tension in the wire is 400 N and the mass per unit length of the wire is 0. 01 kg m−1 , then the minimum common frequency with which all the three parts can vibrate, is (1) 1000 Hz (2) 1100 Hz (3) 100 Hz (4) 110 Hz →