Practice Questions

Q6. What is the minimum energy required to launch a satellite of mass m from the surface of a planet of mass M and radius R in a circular orbit at an altitude of 2R? (1) GmM (2) GmM 2R 3R (3) 5GmM (4) 2GmM 6R 3R

Q6. If the ratio of lengths, radii and Young's moduli of steel and brass wires in the figure are a, b and c respectively, then the corresponding ratio of increase in their lengths is : (1) 3c (2) 2a2c 2ab2 b (3) 3a (4) 2ac 2b2c b2

Q7. Assume that a drop of a liquid evaporates by a decrease in its surface energy so that its temperature remains unchanged. The minimum radius of the drop for this to be possible is. (The surface tension is T , the density of the liquid is ρ and L is its latent heat of vaporisation.) (1) T (2) 2T ρL ρL (3) ρL (4) T √TρL JEE Main 2013 (07 Apr) JEE Main Previous Year Paper

Q7. A uniform wire (Young's modulus 2 × 1011Nm−2 ) is subjected to longitudinal tensile stress of 5 × 107Nm−2 . If the overall volume change in the wire is 0.02%, the fractional decrease in the radius of the wire is close to: (1) 1.0 × 10−4 (2) 1.5 × 10−4 (3) 0.25 × 10−4 (4) 5 × 10−4

Q7. This question has Statement-1 and Statement- 2 . Of the four choices given after the Statements, choose the one that best describes the two Statetnents. Statement-1: A capillary is dipped in a liquid and liquid rises to a height h in it. As the temperature of the liquid is raised, the height h increases (if the density of the liquid and the angle of contact remain the same). Statement-2: Surface tension of a liquid decreases with the rise in its temperature. (1) Statement-1 is true, Statement-2 is true; (2) Statement-1 is false, Statement- 2 is true. Statement-2 is not the correct explanation for Statement-1. (3) Statement-1 is true, Statement- 2 is false. (4) Statement-1 is true, Statement-2 is true; Statement-2 is the correct explanation for Statement-1.

Q7. A mass of 50 g of water in a closed vessel, with surroundings at a constant temperature takes 2 minutes to cool from 30∘C to 25∘C. A mass of 100 g of another liquid in an identical vessel with identical surroundings takes the same time to cool from 30∘C to 25∘C. The specific heat of the liquid is : (The water equivalent of the vessel is 30 g .) (1) 2.0kcal/kg (2) 7kcal/kg (3) 3kcal/kg (4) 0.5kcal/kg

Q7. A copper wire of length 1.0 m and a steel wire of length 0.5 m having equal cross-sectional areas are joined end to end. The composite wire is stretched by a certain load which stretches the copper wire by 1 mm . If the Young's modulii of copper and steel are respectively 1.0 × 1011 Nm−2 and 2.0 × 1011Nm−2 , the total extension of the composite wire is : (1) 1.75 mm (2) 2.0 mm (3) 1.50 mm (4) 1.25 mm

Q8. A sample of gas expands from V1 to V2 . In which of the following, the work done will be greatest? (1) Same in all processes (2) Isobaric process (3) Isothermal process (4) Adiabatic process

Q8. If a piece of metal is heated to temperature θ and then allowed to cool in a room which is at temperature θ0 , the graph between the temperature T of the metal and time t will be closest to : (1) (2) (3) (4)

Q8. Wax is coated on the inner wall of a capillary tube and the tube is then dipped in water. Then, compared to the unwaxed capillary, the angle of contact θ and the height h upto which water rises change. These changes are : JEE Main 2013 (23 Apr Online) JEE Main Previous Year Paper (1) θ increases and h also increases (2) θ decreases and h also decreases (3) θ increases and h decreases (4) θ decreases and h increases

Q8. On a linear temperature scale Y, water freezes at −160∘Y and boils at −50∘Y. On this Y scale, a temperature of 340 K would be read as : (water freezes at 273 K and boils at 373 K ) (1) −73.7∘Y (2) −233.7∘Y (3) −86.3∘Y (4) −106.3∘Y

Q8. Air of density 1.2 kg m−3 is blowing across the horizontal wings of an aeroplane in such a way that its speeds above and below the wings are 150 ms−1 and 100 ms−1 , respectively. The pressure difference between the upper and lower sides of the wings, is : (1) 60Nm−2 (2) 180Nm−2 (3) 7500Nm−2 (4) 12500Nm−2

Q9. Given that 1 g of water in liquid phase has volume 1 cm3 and in vapour phase 1671 cm3 at atmospheric pressure and the latent heat of vaporization of water is 2256 J/g ; the change in the internal energy in joules for 1 g of water at 373 K when it changes from liquid phase to vapour phase at the same temperature is : (1) 2256 (2) 167 (3) 2089 (4) 1

Q9. In the isothermal expansion of 10 g of gas from volume V to 2 V the work done by the gas is 575 J. What is the root mean square speed of the molecules of the gas at that temperature? (1) 398 m/s (2) 520 m/s (3) 499 m/s (4) 532 m/s JEE Main 2013 (25 Apr Online) JEE Main Previous Year Paper

Q9. The above P −V diagram represents the thermodynamic cycle of an engine, operating with an ideal mono- atomic gas. The amount of heat, extracted from the source in a single cycle, is: (1) ( 112 )P0V0 (2) 4P0V0 (3) P0V0 (4) ( 132 )P0V0

Q9. A thin tube sealed at both ends is 100 cm long. It lies horizontally, the middle 20 cm containing mercury and two equal ends containing air at standard atmospheric pressure. If the tube is now turned to a vertical position, by what amount will the mercury be displaced ? (Given : cross-section of the tube can be assumed to be uniform) (1) 2.95 cm (2) 5.18 cm (3) 8.65 cm (4) 0.0 cm

Q9. Figure shows the variation in temperature (ΔT) with the amount of heat supplied (Q) in an isobaric process corresponding to a monoatomic (M), diatomic (D) and a polyatomic (P) gas. The initial state of all the gases JEE Main 2013 (09 Apr Online) JEE Main Previous Year Paper are the same and the scales for the two axes coincide. Ignoring vibrational degrees of freedom, the lines a, b and c respectively correspond to : (1) P, M and D (2) M, D and P (3) P, D and M (4) D, M and P

Q10.Two charges, each equal to q, are kept at x = −a and x = a on the x-axis. A particle of mass m and charge q0 = −q2 is placed at the origin. If charge q0 is given a small displacement (y << a) along the y-axis, the net force acting on the particle is proportional to : (1) y 1 (2) −1y (3) -y (4) y JEE Main 2013 (07 Apr) JEE Main Previous Year Paper

Q10.An ideal gas at atmospheric pressure is adiabatically compressed so that its density becomes 32 times of its initial value. If the final pressure of gas is 128 atmospheres, the value of ' γ 'of the gas is : (1) 1.5 (2) 1.4 (3) 1.3 (4) 1.6 JEE Main 2013 (22 Apr Online) JEE Main Previous Year Paper

Q10. There are two identical chambers, completely thermally insulated from surroundings. Both chambers have a partition wall dividing the chambers in two compartments. Compartment 1 is filled with an ideal gas and Compartment 3 is filled with a real gas. Compartments 2 and 4 are vacuum. A small hole (orifice) is made in the partition walls and the gases are allowed to expand in vacuum. Statement −1 : No change in the temperature of the gas takes place when ideal gas expands in vacuum. However, the temperature of real gas goes down (cooling) when it expands in vacuum. Statement −2 : The internal energy of an ideal gas is only kinetic. The internal energy of a real gas is kinetic as well as potential. (1) Statement-1 is false and Statement-2 is true. (2) Statement-1 and Statement-2 both are true. Statement-2 is the correct explanation of Statement-1. (3) Statement-1 is true and Statement- 2 is false. (4) Statement-1 and Statement-2 both are true. Statement-2 is not correct explanation of Statement-1.

Q10.A uniform cylinder of length L and mass M having cross-sectional area A is suspended, with its length vertical, from a fixed point by a massless spring, such that it is half submerged in a liquid of density σ at equilibrium position. When the cylinder is given a downward push and released, it starts oscillating vertically with a small amplitude. The time period T of the oscillations of the cylinder will be : (1) M 1/2 (2) Smaller than k (k+Aσg) 2π[ ] 2π√M (3) M 1/2 (4) M 1/2 Larger than (k+Aσg) (k+Aσg) 2π[ ] 2π[ ]

Q10.The ratio of the coefficient of volume expansion of a glass container to that of a viscous liquid kept inside the container is 1 : 4. What fraction of the inner volume of the container should the liquid occupy so that the volume of the remaining vacant space will be same at all temperatures ? (1) 2 : 5 (2) 1 : 4 (3) 1 : 64 (4) 1 : 8 Q11. 500 g of water and 100 g of ice at 0∘C are in a calorimeter whose water equivalent is 40 g.10 g of steam at 100∘C is added to it. Then water in the calorimeter is : (Latent heat of ice = 80cal/g, Latent heat of steam = 540cal/g ) (1) 580 g (2) 590 g (3) 600 g (4) 610 g

Q11.Two simple pendulums of length 1 m and 4 m respectively are both given small displacement in the same direction at the same instant. They will be again in phase after the shorter pendulum has completed number of oscillations equal to: (1) 2 (2) 7 (3) 5 (4) 3 JEE Main 2013 (09 Apr Online) JEE Main Previous Year Paper

Q11.An ideal gas enclosed in a vertical cylindrical container supports a freely moving piston of mass M . The piston and the cylinder have equal cross-sectional area A . When the piston is in equilibrium, the volume of the gas is V0 and its pressure is M0 . The piston is slightly displaced from the equilibrium position and released. Assuming that the system is completely isolated from its surrounding, the piston executes a simple harmonic motion with frequency [Assume the system is in space.] 0 1 (1) (2) . 0 . 2π 1 √MVAγP 0 2π √A2γPMV 0 (3) 1 AγP 0 (4) 1 V 0MP 0 . 2π V 0M 2π A2γ

Q11.In a transverse wave the distance between a crest and neighbouring trough at the same instant is 4.0 cm and the distance between a crest and trough at the same place is 1.0 cm. The next crest appears at the same place after a time interval of 0.4 s. The maximum speed of the vibrating particles in the medium is: (1) 3π 2 cm/s (2) 5π2 cm/s (3) π 2 cm/s (4) 2 π cm/s