Practice Questions

Q9. A stationary observer receives sound from two identical tuning forks, one of which approaches and the other one recedes with the same speed (much less than the speed of sound). The observer hears 2 beats/sec . The oscillation frequency of each tuning fork is v0 = 1400 Hz and the velocity of sound in air is 350 m/s . The speed of each tuning fork is close to: (1) 1 m/s (2) 1m/s 2 (3) 4 1 m/s (4) 81 m/s →

Q10.A gas mixture consists of 3 moles of oxygen and 5 moles of argon at temperature T . Assuming the gases to be ideal and the oxygen bond to be rigid, the total internal energy (in units of RT ) of the mixutre is : (1) 15 (2) 13 (3) 20 (4) 11

Q10.Ten charges are placed on the circumference of a circle of radius R with constant angular separation between successive charges. Alternate charges 1, 3, 5, 7, 9 have charge (+q) each, while 2, 4, 6, 8, 10 have charge (–q) each. The potential V and the electric field E at the centre of the circle are respectively : (Take V = 0 at infinity) (1) V = 10q ; E = 0 (2) V = 0, E = 10q 4πϵ0R 4πϵ0R2 (3) V = 0; E = 0 (4) V = 10q ; E = 10q 4πϵ0R 4πϵ0R2

Q10.A block of mass m attached to a massless spring is performing oscillatory motion of amplitude 'A' on a frictionless horizontal plane. If half of the mass of the block breaks off when it is passing through its equilibrium point, the amplitude of oscillation for the remaining system become ƒA. The value of ƒ is: (1) 1 (2) 1 √2 (3) 1 (4) √2 2

Q10.Assume that the displacement (s) of air is proportional to the pressure difference (Δp) created by a sound wave. Displacement (s) further depends on the speed of sound (v), density of air (ρ) and the frequency (f). If Δp~10 Pa, n~300 m/s, p~1 kg/m3 f~1000Hz, then s will be of the order of (take the multiplicative constant to be 1 ) (1) 1003 mm (2) 10 mm (3) 101 mm (4) 1 mm

Q10.Two gases - argon (atomic radius 0.07nm, atomic weight 40 ) and xenon (atomic radius 0.1nm, atomic weight 140 ) have the same number density and are at the same temperature. The ratio of their respective mean free times is closest to: (1) 3.67 (2) 1.83 (3) 2.3 (4) 4.67

Q10.A particle of mass m and charge q has an initial velocity →v= v0ˆj . If an electric field E = E0ˆi and magnetic → field B = B0ˆi act on the particle, its speed will double after a time (1) 2mv0 (2) 3mv0 qE0 qE0 (3) √3mv0 (4) √2mv0 qE0 qE0

Q10.Three charged particles A , B and C with charges −4q, 2q and −2q are present on the circumference of a circle of radius d. The charged particles A, C and centre O of the circle formed an equilateral triangle as shown JEE Main 2020 (08 Jan Shift 1) JEE Main Previous Year Paper in the figure. The electric field at the point O is (1) √3q (2) 2√3q πε0d2 πε0d2 (3) √3q (4) 3√3q 4πε0d2 4πε0d2 →

Q10.Charges Q1 and Q2 are at points A and B of a right-angled triangle OAB. The resultant electric field at point O is perpendicular to the hypotenuse, then Q1/Q2 is proportional to: (1) x31 (2) x2 x32 x1 (3) x1 (4) x22 x2 x21

Q10.Consider a sphere of radius R which carries a uniform charge density ρ . If a sphere of radius R is carved out 2 −→ −−EA → → of it, as shown, the ratio of magnitude of electric field EA and EB , respectively, at points A and B due to− → EB the remaining portion is: (1) 21 (2) 18 34 34 (3) 17 (4) 18 54 54 + × 10−29 C m at the origin (0,0, 0) . The electric field due

Q10. A parallel plate capacitor has plates of area A separated by distance d between them. It is filled with a dielectric which has a dielectric constant that varies as K(x) = K0(1 + αx) where x is the distance measured from one of the plates. If (αd) << 1, the total capacitance of the system is best given by the expression: (1) AK0ε0 d (1 + αd2 ) (2) AK0ε0d [1 + ( αd2 ) 2] α2d2 (3) AK0ε0 + d (1 + αd) d (1 2 ) (4) AK0ε0 JEE Main 2020 (07 Jan Shift 1) JEE Main Previous Year Paper

Q10.When a particle of mass m is attached to a vertical spring of spring constant k and released, its motion, is described by y(t) = y0 sin2 ωt, where ' y' is measured from the lower end of upstretched spring. Then ω is : (1) 1 (2) 2 √gy0 √gy0 (3) √ 2y0g (4) √2gy0

Q10.Match the thermodynamics processes taking place in a system with the correct conditions. In the table : ΔQ is the heat supplied, ΔW is the work done and ΔU is change in internal energy of the system. Process Condition (I) Adiabatic (A) ΔW = 0 (II) Isothermal (B) ΔQ = 0 (III) Isochoric (C) ΔU ≠0, ΔW ≠0, ΔQ ≠0 (IV) Isobaric (D) ΔU = 0 (1) (I) - (A), (II) - (B), (III) - (D), (IV) - (D) (2) (I) - (B), (II) - (A), (III) - (D), (IV) - (C) (3) (I) - (A), (II) - (A), (III) - (B), (IV) - (C) (4) (I) - (B), (II) - (D), (III) - (A), (IV) - (C)

Q10.An elliptical loop having resistance R, of semi major axis a , and semi minor axis b is placed in a magnetic field as shown in the figure. If the loop is rotated about the x-axis with angular frequency ω, the average power loss in the loop due to Joule heating is : (1) π2a2b2B2ω2 (2) zero 2R (3) π bB ω (4) π2a2b2B2ω2 R R

Q10.A 10 μF capacitor is fully charged to a potential difference of 50 V After removing the source voltage it is connected to an uncharged capacitor in parallel. Now the potential difference across them becomes 20 V . The capacitance of the second capacitor is : (1) 15 μF (2) 30 μF (3) 20 μF (4) 10 μF

Q11.A wire of length L and mass per unit length 6.0 × 10−3 kg m−1 is put under tension of 540 N. Two consecutive frequencies that it resonates at are: 420 Hz and 490 Hz. Then L in meters is : (1) 2.1m (2) 1.1m (3) 8.1m (4) 5.1m

Q11.Model a torch battery of length l to be made up of a thin cylindrical bar of radius a and a concentric thin cylindrical shell of radius b filled in between with an electrolyte of resistivity ρ (see figure). If the battery is connected to a resistance of value R, the maximum Joule heating in R will take place for : JEE Main 2020 (03 Sep Shift 1) JEE Main Previous Year Paper (1) R = 2πℓ(ρ ab ) (2) R = 2πℓln(ρ ba ) (3) R = πℓIn(ρ ab ) (4) R = 2ρπℓln( ba )

Q11.Two identical electric point dipoles have dipole have dipole moments →p1 = pˆi and →p2 = −pˆi and are held on the x-axis at distance ' a ' from each other. When released, they move along the x-axis with the direction of their dipole moments remaining unchanged. If the mass of each dipole is ' m', their speed when they are infinitely far apart is : (1) P 1 (2) P 1 a √ πε0 ma a √ 2πε0 ma (3) P 2 (4) P 3 a √ πε0 ma a √ 2πε0 ma

Q11.The current I1 (in A ) flowing through 1Ω resistor in the following circuit is: (1) 0.4 (2) 0.5 (3) 0.2 (4) 0.25

Q11.In a resonance tube experiment when the tube is filled with water up to a height of 17. 0 cm , from bottom, it resonates with a given tuning fork. When the water level is raised the next resonance with the same tuning fork occurs at a height of 24. 5 cm . If the velocity of sound in air is 330 m s−1, the tuning fork frequency is : (1) 2200 Hz (2) 550 Hz (3) 1100 Hz (4) 3300 Hz

Q11.Consider two charged metallic spheres S1 and S2 of radii R1 and R2, respectively. The electric fields E1 (on S1 ) and E2 (on S2 ) on their surfaces are such that E1 = R1 . Then the ratio V1 (on S1 ) /V2 (on S2 ) of the E2 R2 electrostatic potentials on each sphere is: (1) R1 (2) R1 2 R2 ( R2 ) (3) 3 ( R2R1 ) (4) ( R1R2 )

Q11.A two point charges 4q and –q are fixed on the x -axis at x = −d2 and x = d2 , respectively. If the third point charge ‘ q ’ is taken from the origin to x = d along the semicircle as shown in the figure, the energy of the charge will: JEE Main 2020 (04 Sep Shift 1) JEE Main Previous Year Paper (1) Increase by 3q2 (2) Increase by 2q2 4π∈0d 3π∈0d (3) decrease by q2 (4) decrease by 4q2 4π∈0d 3π∈0d

Q11.An electric dipole of moment →p = (−ˆi −3ˆj 2ˆk) to this dipole at→r= +ˆi + 3ˆj + 5ˆk (note that →r∙→p = 0 ) is parallel to: (1) (+ˆi −3ˆj −2ˆk) (2) (−ˆi + 3ˆj −2ˆk) + (3) (+ˆi + 3ˆj −2ˆk) (4) (−ˆi −3ˆj 2ˆk)

Q11.Concentric metallic hollow spheres of radii R and 4R hold charges Q1 and Q2 respectively. Given that surface charge densities of the concentric spheres are equal, the potential difference V(R) −V(4R) is: (1) Q2 (2) 3Q2 4πε0R 4πε0R (3) 3Q1 (4) 3Q1 16πε0R 4πε0R

Q11.In the circuit shown, charge on the 5μF capacitor is : (1) 18. 00μC (2) 10. 90μC (3) 16. 36μC (4) 5. 45μC