Practice Questions

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)

Q8. This question has Statement 1 and Statement 2. Of the four choices given after the Statements, choose the one that best describes the two Statements. Statement 1: When moment of inertia I of a body rotating about an axis with angular speed ω increases, its angular momentum L is unchanged but the kinetic energy K increases if there is no torque applied on it. Statement 2: L = Iω, kinetic energy of rotation = 12 Iω2 JEE Main 2012 (12 May Online) JEE Main Previous Year Paper (1) Statement 1 is true, Statement 2 is true, Statement (2) Statement 1 is false, Statement 2 is true. 2 is not the correct explanation of Statement 1. (3) Statement 1 is true, Statement 2 is true, Statement (4) Statement 1 is true, Statement 2 is false. 2 is correct explanation of the Statement 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%

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. 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 liquid in a beaker has temperature θ(t) at time t and θ0 is temperature of surroundings, then according to Newton's law of cooling the correct graph between loge (θ −θ0) and t is JEE Main 2012 (Offline) JEE Main Previous Year Paper (1) (2) (3) (4)

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

Q10.The load versus elongation graphs for four wires of same length and made of the same material are shown in the figure. The thinnest wire is represented by the line (1) OA (2) OC (3) OD (4) OB

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.This question has Statement 1 and Statement 2. Of the four choices given after the Statements, choose the one that best describes the two Statements. Statement 1: An inventor claims to have constructed an engine that has an efficiency of 30% when operated between the boiling and freezing points of water. This is not possible. Statement 2: The efficiency of a real engine is always less than the efficiency of a Carnot engine operating between the same two temperatures. (1) Statement 1 is true, Statement 2 is true, (2) Statement 1 is true, Statement 2 is false. Statement 2 is not the correct explanation of Statement 1. (3) Statement 1 is false, Statement 2 is true. (4) Statement 1 is true, Statement 2 is true, Statement 2 is the correct explanation of Statement 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.The door of a working refrigerator is left open in a well insulated room. The temperature of air in the room will (1) decrease (2) increase in winters and decrease in summers (3) remain the same (4) increase

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.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

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.If a simple pendulum has significant amplitude (up to a factor of 1/e of original) only in the period between t = 0s to t = τs, then τ may be called the average life of the pendulum. When the spherical bob of the pendulum suffers a retardation (due to viscous drag) proportional to its velocity, with ' b' as the constant of proportionality, the average life time of the pendulum is (assuming damping is small) in seconds: (1) 0.693 (2) b b (3) 1 (4) 2 b b JEE Main 2012 (Offline) JEE Main Previous Year Paper

Q12.The displacement y(t) = A sin(ωt + ϕ) of a pendulum for ϕ = 2π3 is correctly represented by JEE Main 2012 (19 May Online) JEE Main Previous Year Paper (1) (2) (3) (4)

Q12. n moles of an ideal gas undergo a process A →B as shown in the figure. Maximum temperature of the gas during the process is (1) 9P0V0 (2) 3P0V0 nR 2nR (3) 9P0V02nR (4) 9P0V04nR

Q13.An air column in a pipe, which is closed at one end, will be in resonance wtih a vibrating tuning fork of frequency 264 Hz if the length of the column in cm is (velocity of sound = 330 m/s ) (1) 125.00 (2) 93.75 (3) 62.50 (4) 187.50