Practice Questions

Q13.A mixture of 2 moles of helium gas (atomic mass = 4u) , and 1 mole of argon gas (atomic mass = 40 u) is kept 𝑉𝑟𝑚𝑠ℎ𝑒𝑙𝑖𝑢𝑚 at 300 𝐾 in a container. The ratio of their rms speeds , is close to: 𝑉𝑟𝑚𝑠( 𝑎𝑟𝑔𝑜𝑛) (1) 0.45 (2) 2.24 (3) 0.32 (4) 3.16

Q14.There is a uniform spherically symmetric surface charge density at a distance R0 from the origin. The charge distribution is initially at rest and starts expanding because of mutual repulsion. The figure that represents best the speed V (R(t)) of the distribution as a function of its instantaneous radius R(t) is: (1) (2) (3) (4)

Q14.The given graph shows variation (with distancer from centre) of: (1) Electric field of a uniformly charged sphere (2) Potential of a uniformly charged spherical shell (3) Potential of a uniformly charged sphere (4) Electric field of a uniformly charged spherical shell

Q14.Shown in the figure is a shell made of a conductor. It has inner radius 𝑎 and outer radius 𝑏, and carries charge 𝑄 . At its centre a dipole →𝑝 is placed as shown then: (1) Surface charge density on the inner surface of the (2) Electric field outside the shell is the same as that shell is zero everywhere. of a point charge at the centre of the shell. (3) Surface charge density on the inner surface is (4) Surface charge density on the outer surface 𝑄 ( ) depends on →𝑝. uniform and equal to 2 . 4π𝑎2 JEE Main 2019 (12 Apr Shift 1) JEE Main Previous Year Paper is kept at the origin. The potential and electric field due to this dipole on the 𝑦- axis

Q14.Charge is distributed within a sphere of radius R with a volume charge density ρ(r) = A e−2ra , where A and a r2 are constants. If Q is the total charge of this charge distribution, the radius R is: (1) a 1 (2) 1 a Q Q 2 log( 1− 2πaA ) log( 1− 2πaA ) − 2πaA − 2πaA (3) a log(1 Q ) (4) a2 log(1 Q ) q2(−25 μC) are placed on the x -axis at x = 1 m and x = 4 m

Q14.A parallel plate capacitor with plates of area 1 m2 each, are at a separation of 0.1 m. If the electric field between the plates is 100 N/C, the magnitude of charge on each plate is: (Take ∈0= 8.85 × 10−12 N-m2C 2 ) (1) 8.85 x 10−10C (2) 6.85 x 10−10C (3) 9.85 x 10−10C (4) 7.85 x 10−10C

Q14.A simple pendulum of length 1 m is oscillating with an angular frequency 10rad/s. The support of the pendulum starts oscillating up and down with a small angular frequency of 1rad/s and an amplitude of 10−2 m . The relative change in the angular frequency of the pendulum is best given by : (1) 10−3rad/s (2) 1rad/s (3) 10−1rad/s (4) 10−5rad/s

Q14.Three charges +𝑄, 𝑞, + 𝑄 are placed respectively, at distance, 0, 𝑑/ 2 and 𝑑 from the origin, on the 𝑥 -axis. If the net force experienced by +𝑄, placed at 𝑥= 0, is zero, then value of 𝑞 is: (1) +𝑄/ 2 (2) +𝑄/ 4 (3) -𝑄/ 4 (4) -𝑄/ 2

Q14.A string is clamped at both the ends and it is vibrating in its 4th harmonic. The equation of the stationary wave is y = 0.3 sin(0.157x) cos(200πt). The length of the string is JEE Main 2019 (09 Apr Shift 1) JEE Main Previous Year Paper (All quantities are in SI units.) (1) 20 m (2) 60 m (3) 40 m (4) 80 m

Q14.A small speaker delivers 2 W of audio output. At what distance from the speaker will one detect 120 dB intensity sound? [Given reference intensity of sound as 10−12 W/m2 ] (1) 40 cm (2) 20 cm (3) 10 cm (4) 30 cm

Q14.The bob of a simple pendulum has mass 2 g and a charge of 5.0 μC . It is at rest in a uniform horizontal electric field of intensity 2000 V / m At equilibrium, the angle that the pendulum makes with the vertical is: take g = 10 m / s2 (1) tan-10.2 (2) tan-12.0 (3) tan-10.5 (4) tan-15.0

Q14.Figure shows charge (q) versus voltage (V) graph for series and parallel combination of two given capacitors. The capacitances are: (1) 60 μF and 40 μF (2) 50 μF and 30 μF (3) 20 μF and 30 μF (4) 40 μF and 10 μF

Q14.A cylindrical plastic bottle of negligible mass is filled with 310 ml of water and left floating in a pond with still water. If pressed downward slightly and released, it starts performing simple harmonic motion at angular frequency ω. If the radius of the bottle is 2.5 cm then ω is close to: ( density of water = 103kg/m3) (1) 5.00 rad sec−1 (2) 2.50 rad sec−1 (3) 7.9 rad sec−1 (4) 3.75 rad sec−1

Q14.One mole of an ideal gas passes through a process where pressure and volume obey the relation 1 Vo 2 P = Po1 - . Here Po and Vo are constants. Calculate the change in the temperature of the gas if its volume 2 V changes from Vo to 2Vo . 1 P0V0 5 P0V0 (1) (2) 4 R 4 R 1 P0V0 3 P0V0 (3) (4) 2 R 4 R

Q14.A string 2.0 m long and fixed at its ends is driven by a 240 Hz vibrator. The string vibrates in its third harmonic mode. The speed of the wave and its fundamental frequency is (1) 320 m s−1, 120 Hz (2) 320 m s−1, 80 Hz (3) 180 m s−1, 80 Hz (4) 180 m s−1, 120 Hz

Q14.Two electric dipoles, A, B with respective dipole moments dA→ = −4qaˆi and dB→ = −2qaˆi are placed on the x - axis with a separation R, as shown in the figure The distance from A at which both of them produce the same potential is: (1) R (2) √2R √2 −1 √2−1 (3) √2 R (4) R √2+1 √2+1 JEE Main 2019 (10 Jan Shift 1) JEE Main Previous Year Paper

Q14.A positive point charge is released from rest at a distance r0 from a positive line charge with uniform charge density. The speed ( v ) of the point charge, as a function of instantaneous distance r from line charge, is proportional to (1) v ∝r (2) v r r0 ∝√ln⁡r0 +r (3) v ∝ln⁡r (4) r0 v ∝e r0

Q15.Four point charges −q, + q, + q and −q are placed on y-axis at y = −2d, y = −d, and y = +2d, respectively. The magnitude of the electric field E at a point on the x-axis at x = D, with D ≫d, will behave JEE Main 2019 (09 Apr Shift 2) JEE Main Previous Year Paper as: (1) E ∝ 1 (2) E ∝ D1 D4 (3) E ∝ 1 (4) E ∝ 1 D3 D2

Q15.A closed organ pipe has a fundamental frequency of 1.5 kHz. The number of overtones that can be distinctly heard by a person with this organ pipe will be (Assume that the highest frequency a person can hear is 20,000 Hz). (1) 7 (2) 4 (3) 6 (4) 5

Q15.When heat Q is supplied to a diatomic gas of rigid molecules, at constant volume its temperature increases by ∆T . The heat required to produce the same change in temperature, at a constant pressure is: (1) 3 (2) 7 2Q 5Q 5 2 (3) 3Q (4) 3Q

Q15.Three charges Q, +y and +q are placed at the vertices of a right-angle isosceles triangle as shown below. The net electrostatic energy of the configuration is zero, if the value of Q is (1) +q (2) −√2q √2+1 (3) −q (4) −2q 1+√2

Q15.An electric dipole is formed by two equal and opposite charges q with separation d . The charges have same mass m. It is kept in a uniform electric field E . If it is slightly rotated from its equilibrium orientation, then its angular frequency 𝜔 is: (1) qE (2) 2qE 2√ md √ md (3) qE (4) qE √ 2md √ md

Q15.A current of 5 A passes through a copper conductor (resistivity = 1.7 × 10−8 Ω m ) of radius of cross-section 5 mm . Find the mobility of the charges if their drift velocity is 1.1 × 10−3 ms−1 . (1) 1.5 m2 V−1 s−1 (2) 1.8 m2 V−1 s−1 (3) 1.0 m2 V−1 s−1 (4) 1.3 m2 V−1 s−1

Q15.For a uniformly charged ring of radius 𝑅, the electric field on its axis has the largest magnitude at a distance ℎ from its centre. Then value of ℎ is: (1) 𝑅 (2) 𝑅 √2 √5 (3) 𝑅√2 (4) 𝑅

Q15.Two sources of sound S1 and S2 produce sound waves of same frequency 660 Hz. A listener is moving from source S1 towards S2 with a constant speed u0 m/s and he hears 10 beats/s. The velocity of sound is 330 m/s. Then, u0 equals: (1) 10.0 m/s (2) 2.5 m/s (3) 5.5 m/s (4) 15.0 m/s