Practice Questions

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

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.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

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.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

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.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.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 tuning fork vibrates with frequency 256 Hz and gives one best per second with the third normal mode of vibration of an open pipe. What is the length of the pipe? (Speed of sound of air is 340 ms−1 ) JEE Main 2018 (15 Apr Shift 1 Online) JEE Main Previous Year Paper (1) (a) 190 cm (2) 180 cm (3) 220 cm (4) 200 cm

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.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 a square surface of side length a. The electric flux through the square surface due to the charge would be? (1) Q (2) Q 6ϵ0 2ϵ0 (3) Q (4) Q 3ϵ0 ϵ0 JEE Main 2018 (15 Apr) JEE Main Previous Year Paper

Q14.Two sitar strings, A and B playing the note ' Dha' are slightly out of tune and produce beats of frequency 5 Hz . The tension of the string B is slightly increased and the beat frequency is found to decrease by 3 Hz. If the frequency of A is 425 Hz. The original frequency of B is (1) 428 Hz (2) 430 Hz (3) 422 Hz (4) 420 Hz

Q14.A granite rod of 60 cm length is clamped at its middle point and is set into longitudinal vibrations. The density of granite is 2.7 × 103 kg m−3 and its Young's modulus is 9.27 × 1010 Pa. What will be the fundamental frequency of the longitudinal vibrations? (1) 7. 5 kHz (2) 5 kHz (3) 2. 5 kHz (4) 10 kHz

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

Q15.Two identical conducting spheres A and B carry an equal charges. They are separated by a distance much larger than their diameters, and the force between them is F . A third identical conducting sphere, C , is uncharged. Sphere C is first touched to A , then to B, and then removed. As a result, the force between A and B would be equal to: (1) 3F (2) F 4 2 (3) 3F (4) F 8

Q15.Three concentric metal shells A, B and C of respective radii a, b and c (a < b < c) have surface charge densities +σ, −σ and +σ respectively. The potential of shell B is: (1) + + ε0 σ [ b2−c2c a] (2) ε0σ [ a2−b2a c] (3) + + ε0 σ [ a2−b2b c] (4) ε0σ [ b2−c2b a]

Q16.In the following circuit the switch S is closed at t = 0. The charge on the capacitor C1 as a function of time will be given by (Ceq = C1+C1C2C2 ) (1) C1E [1 −exp(−tRC1 )] (2) CeqE exp[− RCeqt ] (3) CeqE [1 −exp(− RCeqt )] (4) C2E [1 −exp(− RC2t )]

Q16.In a meter bridge as shown in the figure, it is given that resistance Y = 12.5 Ω and that the balance is obtained at a distance 39. 5 cm from end A (by jockey J ). After interchanging the resistances X and Y a new balance point is found at a distance l2 from end A. What are the values of X (in Ω) and l2 ? (1) 19. 15 Ω and 39. 5 cm (2) 8. 16 Ω and 60. 5 cm (3) 8. 16 Ω and 39. 5 cm (4) 19. 15 Ω and 60. 5 cm

Q16.A parallel plate capacitor of capacitance 90 pF is connected to a battery of EMF 20 V. If a dielectric material of dielectric constant K = 53 is inserted between the plates, the magnitude of the induced charge will be: (1) 0. 9 nC (2) 1. 2 nC (3) 0. 3 nC (4) 2. 4 nC

Q16.A copper rod of cross-sectional area A carries a uniform current I through it. At temperature T, if the volume charge density of the rod is ρ, how long will the charges take to travel a distance d ? (1) 2ρdA (2) 2ρdA IT I (3) ρdA (4) ρdA I IT