Practice Questions

Q6. A spring is compressed between two blocks of masses m1 and m2 placed on a horizontal frictionless surface as shown in the figure. When the blocks are released, they have initial velocity of v1 and v2 as shown. The blocks travel distances x1 and x2 respectively before coming to rest. The ratio ( x1x2 ) is (1) m2 (2) m1 m1 m2 (3) √m2m1 (4) √m1m2

Q6. A moving particle of mass m, makes a head on elastic collision with another particle of mass 2m, which is initially at rest. The percentage loss in energy of the colliding particle on collision, is close to (1) 33% (2) 67% (3) 90% (4) 10%

Q6. A circular hole of diameter R is cut from a disc of mass M and radius R; the circumference of the cut passes through the centre of the disc. The moment of inertia of the remaining portion of the disc about an axis perpendicular to the disc and passing through its centre is (1) ( 1532 )MR2 (2) ( 18 )MR2 (3) ( 83 )MR2 (4) ( 1332 )MR2

Q6. The mass of a spaceship is 1000 kg. It is to be launched from the earth's surface out into free space. The value of ' g ' and ' R ' (radius of earth) are 10 m/s2 and 6400 km respectively. The required energy for this work will be ; (1) 6.4 × 1011 Joules (2) 6.4 × 108 Joules (3) 6.4 × 109 Joules (4) 6.4 × 1010 Joules JEE Main 2012 (Offline) JEE Main Previous Year Paper

Q6. A stone of mass m, tied to the end of a string, is whirled around in a circle on a horizontal frictionless table. The length of the string is reduced gradually keeping the angular momentum of the stone about the centre of the circle constant. Then, the tension in the string is given by T = Arn , where A is a constant, r is the instantaneous radius of the circle. The value of n is equal to (1) −1 (2) −2 (3) −4 (4) −3

Q7. A solid sphere is rolling on a surface as shown in figure, with a translational velocity v m s−1 . If it is to climb the inclined surface continuing to roll without slipping, then minimum velocity for this to happen is (1) √2gh (2) √75 gh (3) (4) gh gh √72 √107

Q7. A steel wire can sustain 100 kg weight without breaking. If the wire is cut into two equal parts, each part can sustain a weight of (1) 50 kg (2) 400 kg (3) 100 kg (4) 200 kg

Q7. A thin liquid film formed between a U-shaped wire and a light slider supports a weight of 1.5 × 10−2 N (see figure). The length of the slider is 30 cm and its weight negligible. The surface tension of the liquid film is (1) 0.0125 Nm−1 (2) 0.1 Nm−1 (3) 0.05 Nm−1 (4) 0.025 Nm−1

Q7. A solid sphere having mass m and radius r rolls down an inclined plane. Then its kinetic energy is (1) 5 rotational and 2 translational (2) 2 rotational and 5 translational 7 7 7 7 (3) 2 rotational and 3 translational (4) 1 rotational and 1 translational 5 5 2 2 JEE Main 2012 (07 May Online) JEE Main Previous Year Paper

Q8. A wooden wheel of radius R is made of two semicircular parts (see figure); The two parts are held together by a ring made of a metal strip of cross sectional area S and length L. L is slightly less than 2πR. To fit the ring on the wheel, it is heated so that its temperature rises by ΔT and it just steps over the wheel. As it cools down to surrounding temperature, it presses the semicircular parts together. If the coefficient of linear expansion of the metal is α, and its Youngs' modulus is Y , the force that one part of the wheel applies on the other part is : (1) 2πSYαΔT (2) SYαΔT (3) πSYαΔT (4) 2SYαΔT

Q8. A large number of droplets, each of radius, r coalesce to form a bigger drop of radius, R. An engineer designs a machine so that the energy released in this process is converted into the kinetic energy of the drop. Velocity of the drop is ( T = surface tension, ρ = density) JEE Main 2012 (19 May Online) JEE Main Previous Year Paper (1) T 1 1/2 (2) 6T 1 1/2 [ ρ ( r −1R )] [ ρ ( r −1R )] (3) 3T 1 1/2 (4) 2T 1 1/2 [ ρ ( r −1R )] [ ρ ( r −1R )]

Q8. A point particle is held on the axis of a ring of mass m and radius r at a distance r from its centre C . When released, it reaches C under the gravitational attraction of the ring. Its speed at C will be (1) √2Gmr (√2 −1 (2) √Gmr − √2Gmr r (1 √2 ) (3) √2Gm 1 (4)

Q9. A large cylindrical rod of length L is made by joining two identical rods of copper and steel of length ( L2 ) each. The rods are completely insulated from the surroundings. If the free end of copper rod is maintained at 100∘C and that of steel at 0∘C then the temperature of junction is (Thermal conductivity of copper is 9 times that of steel) (1) 90∘C (2) 50∘C (3) 10∘C (4) 67∘C

Q9. Assuming the earth to be a sphere of uniform density, the acceleration due to gravity inside the earth at a distance of r from the centre is proportional to (1) r (2) r−1 (3) r2 (4) r−2

Q9. The terminal velocity of a small sphere of radius a in a viscous liquid is proportional to JEE Main 2012 (26 May Online) JEE Main Previous Year Paper (1) a2 (2) a3 (3) a (4) a−1

Q9. A structural steel rod has a radius of 10 mm and length of 1.0 m. A 100kN force stretches it along its length. Young's modulus of structural steel is 2 × 1011Nm−2 . The percentage strain is about (1) 0.16% (2) 0.32% (3) 0.08% (4) 0.24%

Q10.Helium gas goes through a cycle ABCDA (consisting of two isochoric and two isobaric lines) as shown in figure. Efficiency of this cycle is nearly: (Assume the gas to be close to ideal gas) (1) 15.4% (2) 9.1% (3) 10.5% (4) 12.5%

Q10.Water is flowing through a horizontal tube having cross-sectional areas of its two ends being A and A′ such that the ratio A/A′ is 5 . If the pressure difference of water between the two ends is 3× 105 N m−2 , the velocity of water with which it enters the tube will be (neglect gravity effects) (1) 5 m s−1 (2) 10 m s−1 (3) 25 m s−1 (4) 50√10 m s−1

Q10.In a cylindrical water tank, there are two small holes A and B on the wall at a depth of h1 , from the surface of water and at a height of h2 from the bottom of water tank. Surface of water is at height of h2 from the bottom of water tank. Surface of water is at heigh H from the bottom of water tank. Water coming out from both holes strikes the ground at the same point S . Find the ratio of h1 and h2 (1) Depends on H (2) 1 : 1 (3) 2 : 2 (4) 1 : 2

Q11.The pressure of an ideal gas varies with volume as P = αV , where α is a constant. One mole of the gas is allowed to undergo expansion such that its volume becomes ' m ' times its initial volume. The work done by the gas in the process is (1) αV 2 (m2 −1) (2) α2V2 2 (m2 −1) (3) α 2 (m2 −1) (4) αV2 2 (m2 −1)

Q11.A square hole of side length ℓ is made at a depth of h and a circular hole of radius r is made at a depth of 4 h from the surface of water in a water tank kept on a horizontal surface. If ℓ<< h, r << h and the rate of water flow from the holes is the same, then r is equal to JEE Main 2012 (07 May Online) JEE Main Previous Year Paper (1) ℓ (2) ℓ √2π √3π (3) ℓ (4) ℓ 3π 2π

Q11.A given ideal gas with γ = Cp = 1.5 at a temperature T . If the gas is compressed adiabatically to one-fourth Cv of its initial volume, the final temperature will be (1) 2√2T (2) 4T (3) 2T (4) 8T

Q11.A Carnot engine, whose efficiency is 40%, takes in heat from a source maintained at a temperature of 500 K It is desired to have an engine of efficiency 60%. Then, the intake temperature for the same exhaust (sink) temperature must be (1) efficiency of Carnot engine cannot be made (2) 1200 K larger than 50% (3) 750 K (4) 600 K

Q12.The heat radiated per unit area in 1 hour by a furnace whose temperature is 3000 K is (σ = 5.7× 10−8 W m−2 K−4 ) (1) 1.7 × 1010 J (2) 1.1 × 1012 J (3) 2.8 × 108 J (4) 4.6 × 106 J

Q12.An ideal monatomic gas with pressure P , volume V and temperature T is expanded isothermally to a volume 2V and a final pressure Pi . If the same gas is expanded adiabatically to a volume 2 V, the final pressure is Pa . The ratio Pa is Pi (1) 2−1/3 (2) 21/36 (3) 22/3 (4) 2−2/3