Practice Questions

Q9. A thin uniform tube is bent into a circle of radius r in the vertical plane. Equal volumes of two immiscible liquids, Whose densities are ρ1 and ρ2 (ρ1 > ρ2 ), fill half the circle. The angle θ between the radius vector passing through the common interface and the vertical is: θ = (1) θ = tan−1 π2 ( ρ1−ρ2ρ1+ρ2 ) (2) tan−1[( ρ1+ρ2ρ1−ρ2 )] θ = (3) θ = tan−1 π2 ( ρ2ρ1 ) (4) tan−1π( ρ2ρ1 )

Q9. When an air bubble of radius r rises from the bottom to the surface of a lake, its radius becomes 5r . Taking the 4 atmospheric pressure to be equal to 10 m height of water column, the depth of the lake would approximately be (ignore the surface tension and the effect of temperature): (1) 10.5 m (2) 8.7 m (3) 11.2 m (4) 9.5 m

Q9. From a uniform circular disc of radius R and mass 9 M, a small disc of radius R is removed as shown in the 3 figure. The moment of inertia of the remaining disc about an axis perpendicular to the plane of the disc and passing through centre of disc is: (1) 37 MR2 (2) 4MR2 9 (3) 40 MR2 (4) 10MR2 9

Q9. One mole of an ideal monatomic gas is taken along the path ABCA as shown in the PV diagram. The maximum temperature attained by the gas along the path BC is given by: (1) 25 P0V0 (2) 5 P0V0 4 R 8 R (3) 25 P0V0 (4) 25 P0V0 8 R 16 R

Q9. A thin uniform tube is bent into a circle of radius r in the virtical plane. Equal volumes of two immiscible liquids, whose densities are ρ1 and ρ2 (ρ1 > ρ2) fill half the circle. The angle θ between the radius vector passing through the common interface and the vertical is π (1) θ = tan−1 2 (2) θ = tan−1 π2 [ ( ρ1−ρ2ρ1+ρ2 )] ( ρ1+ρ2ρ1−ρ2 ) (3) θ = tan−1 π ρ2 ρ1 (4) θ = tan−1 π2 ρ2ρ1 ( ) ( )

Q10.Two moles of helium are mixed with n moles of hydrogen. If Cp = 32 for the mixture then the value of n is, Cv (1) 1 (2) 3 (3) 2 (4) 3 2

Q10.A particle is moving with a uniform speed in a circular orbit of radius R in a central force inversely proportional to the nth power of R. If the period of rotation of the particle is T, then: (1) T ∝Rn/2 (2) T ∝R3/2 for any n (3) T ∝R n2 +1 (4) T ∝R n+12

Q10.One mole of an ideal monatomic gas is compressed isothermally in a rigid vessel to double its pressure at room temperature, 27oC . The magnitude of work done on the gas will be: (1) 300R (2) 300R ln 2 (3) 300 ln 6 (4) 300R ln 7

Q10.A body takes 10 minutes to cool from 60∘C to 50∘C. The temperature of surroundings is constant at 25∘C. Then, the temperature of the body after next 10 minutes will be approximately (1) 43∘C (2) 47∘C (3) 41∘C (4) 45∘C

Q10.A Carnot's engine works as a refrigerator between 250 K and 300 K . It receives 500cal heat from the reservoir at the lower temperature. The amount of work done in each cycle to operate the refrigerator is: (1) 420 J (2) 2100 J (3) 772 J (4) 2520 J

Q11.One mole of an ideal monoatomic gas is compressed isothermally in a rigid vessel to double its pressure at room temperature, 27∘C. The work done on the gas will be: (1) 300R ln 6 (2) 300R (3) 300R ln 7 (4) 300R ln 2

Q11.A solid sphere of radius r made of a soft material of bulk modulus K is surrounded by a liquid in a cylindrical container. A massless piston of area a floats on the surface of the liquid, covering entire cross-section of JEE Main 2018 (08 Apr) JEE Main Previous Year Paper cylindrical container. When a mass m is placed on the surface of the piston to compress the liquid, the fractional decrement in the radius of the sphere ( drr ) , is: (1) mg (2) Ka Ka mg (3) Ka (4) mg 3mg 3Ka

Q11.A Carnot's engine works like a refrigerator between 250 K and 300 K . It receives 500 cal heat from the reservoir at a lower temperature. The amount of work done in each cycle to operate the refrigerator is, (1) 772 J (2) 420 J (3) 2100 J (4) 2520 J

Q11.Two Carnot engines A and B are operated in series. Engine A receives heat from a reservoir at 600 K and rejects heat to a reservoir at temperature T. Engine B receives heat rejected by engine A and in turn rejects it to JEE Main 2018 (15 Apr Shift 2 Online) JEE Main Previous Year Paper a reservoir at 100 K. If the efficiencies of the two engines A and B are represented by ηA and ηB respectively, then what is the value of ηA ηB (1) 12 (2) 12 7 5 (3) 5 (4) 7 12 12

Q11.An oscillator of mass M is at rest in its equilibrium position in a potential, V = 12 k(x –X)2 . A particle of mass m comes from the right with speed u and collides completely inelastic with M and sticks to it. This process repeats every time the oscillator crosses its equilibrium position. The amplitude of oscillations after 13 collisions is: (M = 10, m = 5, u = 1, k = 1) (1) 2 (2) 1 3 √3 2 (3) √35 (4) 1

Q12.The value closest to the thermal velocity of a Helium atom at room temperature (300 K) in ms−1 is: [kB = 1.4 × 10−23 J/K; mHe = 7 × 10−27 kg] (1) 1.3 × 104 (2) 1.3 × 105 (3) 1.3 × 102 (4) 1.3 × 103

Q12.Two moles of an ideal monoatomic gas occupies a volume V at 27oC . The gas expands adiabatically to a volume 2V . Calculate (a) the final temperature of the gas and (b) change in its internal energy. (1) (a)195 K (b)2.7 kJ (2) (a)189 K (b)2.7 kJ (3) (a)195 K (b) −2.7 kJ (4) (a)189 K (b) −2.7 kJ

Q12.A particle executes simple harmonic motion and it is located at x = a, b and c at time t0, 2t0 and 3t0 respectively. The frequency of the oscillation is: (1) 2πt0 1 cos−1( a+c2b ) (2) 2πt01 cos−1( a+2b3c ) (3) 2πt0 1 cos−1( a+b2c ) (4) 2πt01 cos−1( 2a+3cb )

Q12.A body of mass M and charge q is connected to a spring of spring constant k. It is oscillating along x-direction about its equilibrium position in the horizontal plane, taken to be at x = 0, with an amplitude A. An electric field E is applied along the x-direction. Which of the following statements is correct? (1) The total energy of the system is (2) The new equilibrium position is at a distance 2qE k x = 0 2 1 mω2A2 + 12 q2E2k from (3) The new equilibrium position is at a distance qE (4) The total energy of the system is 2k from x = 0 1 . 2 mω2A2 −12 q2E2k

Q13.A body of mass M and charge q is connected to a spring of spring constant k. It is oscillating along x-direction about its equilibrium position, taken to be at x = 0, with an amplitude A. An electric field E is applied along the x-direction. Which of the following statements is correct? (1) The total energy of the system is (2) The new equilibrium position is at a distance: 2qE from x = 0 k 2 1 1 q2E mω2A2 + 2 2 k (3) The new equilibrium position is at a distance: qE (4) The total energy of the system is 2k from x = 0 1 2 mω2A2 −12 q2E2k

Q13.The end correction of a resonance column is 1 cm . If the shortest length resonating with the tuning fork is 10 cm, the next resonating length should be (1) 32 cm (2) 40 cm (3) 28 cm (4) 36 cm JEE Main 2018 (16 Apr Online) JEE Main Previous Year Paper

Q13.Two simple harmonic motions, as shown, are at right angles. They are combined to form Lissajous figures. x(t) = A sin(at + δ) y(t) = B sin(bt) Identify the correct match below (1) Parameters: A = B, a = 2 b; δ = π2 ; Curve: (2) Parameters: A = B, a = b; δ = π2 ; Curve: Line Circle (3) Parameters: A ≠B, a = b; δ = π2 ; Curve: Ellipse(4) Parameters: A ≠B, a = b; δ = 0; Curve: Parabola Q14.5 beats/ second are heard when a turning fork is sounded with a sonometer wire under tension, when the length of the sonometer wire is either 0.95 m or 1 m. The frequency of the fork will be: (1) 195 Hz (2) 251 Hz (3) 150 Hz (4) 300 Hz Q15.[12] A solid ball of radius R has a charge density ρ given by ρ = ρ0 (1 −rR ) for 0 ≤r ≤R. The electric field outside the ball is: (1) ρ0R3 (2) 4ρ0R3 ε0r2 3ε0r2 (3) 3ρ0R3 (4) ρ0R3 4ε0r2 12ε0r2

Q13.A tuning fork vibrates with frequency 256 Hz and gives one beat per second with the third normal mode of vibration of an open pipe. What is the length of the pipe? (speed of sound in air is 340 m s−1 ) (1) 220 cm (2) 200 cm (3) 190 cm (4) 180 cm

Q13.A silver atom in a solid oscillates in simple harmonic motion in some direction with a frequency of 1012 s−1 . What is the force constant of the bonds connecting one atom with the other? (Mole wt. of silver, = 108 g mol−1 and Avogadro number = 6.02 × 1023 ) (1) 5.5 N m−1 (2) 6.4 N m−1 (3) 7. 1 N m−1 (4) 2.2 N m−1

Q14.A charge Q is placed at a distance a/2 above the centre of the square surface of edge a as shown in the figure. The electric flux through the square surface is: (1) Q (2) Q 3ε0 6ε0 (3) Q (4) Q 2ε0 ε0