Practice Questions

Q10.In a simple harmonic oscillation, what fraction of total mechanical energy is in the form of kinetic energy, when the particle is midway between mean and extreme position. (1) 1 (2) 3 2 4 (3) 1 (4) 1 3 4

Q11.For a body executing S.H.M. : (a) Potential energy is always equal to its 𝐾. 𝐸. (b) Average potential and kinetic energy over any given time interval are always equal. (c) Sum of the kinetic and potential energy at any point of time is constant. (d) Average 𝐾. 𝐸. in one time period is equal to average potential energy in one time period. Choose the most appropriate option from the options given below : (1) (c) and (d) (2) only (c) (3) only (b) (4) (b) and (c)

Q11. Calculate the amount of charge on capacitor of 4 μF. The internal resistance of battery is 1Ω : (1) 4 μC (2) 8 μC (3) 16 μC (4) zero

Q11.Two ideal electric dipoles A and B, having their dipole moment p1 and p2 respectively are placed on a plane with their centres at O as shown in the figure. At point C on the axis of dipole A, the resultant electric field is making an angle of 37° with the axis. The ratio of the dipole moment of A and B, p1 is : ( take sin 37°= 53 ) p2 (1) 3 (2) 3 8 2 (3) 2 (4) 4 3 3

Q11.A sound wave of frequency 245 Hz travels with the speed of 300 m s−1 along the positive x-axis. Each point of the wave moves to and fro through a total distance of 6 cm . What will be the mathematical expression of this travelling wave? (1) Y (x, t) = 0. 03[sin 5. 1x −(0. 2 × 103)t] (2) Y (x, t) = 0. 06[sin 5. 1x −(1. 5 × 103)t] (3) Y (x, t) = 0. 06[sin 0. 8x −(0. 5 × 103)t] (4) Y (x, t) = 0. 03[sin 5. 1x −(1. 5 × 103)t]

Q11.For what value of displacement the kinetic energy and potential energy of a simple harmonic oscillation become equal? JEE Main 2021 (17 Mar Shift 1) JEE Main Previous Year Paper (1) x = 0 (2) x = ±A (3) x = ± A (4) x = A2 √2

Q11.In the given figure, a mass 𝑀 is attached to a horizontal spring which is fixed on one side to a rigid support. The spring constant of the spring is 𝑘. The mass oscillates on a frictionless surface with time period 𝑇 and amplitude 𝐴. When the mass is in equilibrium position, as shown in the figure, another mass 𝑚 is gently fixed upon it. The new amplitude of oscillation will be: (1) 𝑀+ 𝑚 (2) 𝑀 𝐴√ 𝑀 𝐴√ 𝑀- 𝑚 (3) 𝑀- 𝑚 (4) 𝑀 𝐴√ 𝑀 𝐴√ 𝑀+ 𝑚

Q11.A particle executes S.H.M., the graph of velocity as a function of displacement is : (1) a circle (2) a helix (3) a parabola (4) an ellipse

Q11.An object of mass 0. 5 kg is executing simple harmonic motion. It amplitude is 5 cm and time period (T) is 0. 2 s . What will be the potential energy of the object at an instant t = T4 s starting from mean position. Assume that the initial phase of the oscillation is zero. (1) 0. 62 J (2) 6. 2 × 10−3 J (3) 1. 2 × 103 J (4) 6. 2 × 103 J

Q11.In a scries LCR resonance circuit, if we change the resistance only, from a lower to higher value : JEE Main 2021 (18 Mar Shift 1) JEE Main Previous Year Paper (1) The bandwidth of resonance circuit will increase. (2) The resonance frequency will increase. (3) The quality factor will increase. (4) The quality factor and the resonance frequency will remain constant.

Q11.A proton, a deuteron and an α particle are moving with same momentum in a uniform magnetic field. The ratio of magnetic forces acting on them ______ is and their speed is ______ in the ratio. (1) 2 : 1 : 1 and 4 : 2 : 1 (2) 1 : 2 : 4 and 2 : 1 : 1 (3) 4 : 2 : 1 and 2 : 1 : 1 (4) 1 : 2 : 4 and 1 : 1 : 2

Q11.Three capacitors C1 = 2 μF, C2 = 6 μF and C3 = 12 μF are connected as shown in the figure. Find the ratio of the charges on capacitors C1, C2 and C3 respectively. JEE Main 2021 (27 Aug Shift 2) JEE Main Previous Year Paper (1) 3 : 4 : 4 (2) 2 : 3 : 3 (3) 2 : 1 : 1 (4) 1 : 2 : 2

Q11.An electron with kinetic energy K1 enters between parallel plates of a capacitor at an angle α with the plates. It leaves the plates at angle β with kinetic energy K2. Then the ratio of kinetic energies K1 : K2 will be : (1) sin2 β (2) cos β cos2 α sin α (3) cos β (4) cos2 β cos α cos2 α

Q11.Assume that a tunnel is dug along a chord of the earth, at a perpendicular distance R2 from the earth's centre, where R is the radius of the earth. The wall of the tunnel is frictionless. If a particle is released in this tunnel, it will execute a simple harmonic motion with a time period: (1) 1 (2) 2π √gR 2π√Rg (3) 2πRg (4) Image is virtual, opposite side of convex mirror.

Q11.A cube is placed inside an electric field, →𝐸= 150𝑦2^j The side of the cube is 0 . 5 m and is placed in the field as shown in the given figure. The charge inside the cube is: (1) 8 . 3 × 10-11C (2) 3 . 8 × 10-11C (3) 3 . 8 × 10-12C (4) 8 . 3 × 10-12C

Q11.A charge Q is moving dl distance in the magnetic field B. Find the value of work done by B. (1) 1 (2) Infinite (3) Zero (4) −1 → x . A square loop of side d is placed with its edges along

Q11.For changing the capacitance of a given paralle plate capacitor, a dielectric material of dielectric constant K is used, which has the same area as the plates of the capacitor. The thickness of the dielectric slab is 3 d, where d 4 is the separation between the plates of parallel plate capacitor. The new capacitance C ′ in terms of original capacitance C0 is given by the following relation : (1) C ′ = 3+K4K C0 (2) C ′ = 4+K3 C0 (3) C ′ = K+34K C0 (4) C ′ = 3+K4 C0

Q11.What equal length of an iron wire and a copper-nickel alloy wire, each of 2 mm diameter connected parallel to give an equivalent resistance of 3 Ω? (Given resistivities of iron and copper-nickel alloy wire are 12 μΩ cm and 51 μΩ cm respectively) (1) 97 m (2) 110 m (3) 90 m (4) 82 m

Q11.Consider a galvanometer shunted with 5 Ω resistance and 2% of current passes through it. What is the resistance of the given galvanometer? (1) 245 Ω (2) 344 Ω (3) 300 Ω (4) 226 Ω

Q11. The value of current in the 6 Ω resistance is: (1) 4 A (2) 8 A (3) 10 A (4) 6 A

Q11.Two identical tennis balls each having mass m and charge q are suspended from a fixed point by threads of length l. What is the equilibrium separation when each thread makes a small angle θ with the vertical? (1) q2l 12 (2) q2l 13 x = x = ( 2πε0mg ) ( 2πε0mg ) (3) q2l2 13 (4) q2l2 13 x = x = ( 2πε0 m2 g ) ( 2πε0m2g2 )

Q11.The two thin coaxial rings, each of radius a and having charges +Q and −Q respectively are separated by a distance of s. The potential difference between the centres of the two rings is : JEE Main 2021 (26 Aug Shift 2) JEE Main Previous Year Paper (1) − − 2πε0 1 ] Q [ a1 1 ] (2) 4πε0Q [ a1 √s2+a2 √s2+a2 (3) + + 4πε0 1 ] Q [ a1 1 ] (4) 2πε0Q [ a1 √s2+a2 √s2+a2

Q11.The function of time representing a simple harmonic motion with a period of π is : ω (1) sin(ωt) + cos(ωt) (2) cos(ωt) + cos(2ωt) + cos(3ωt) (3) sin2(ωt) (4) 3 cos( π4 −2ωt)

Q12.If qf is the free charge on the capacitor plates and qb is the bound charge on the dielectric slab of dielectric constant k placed between the capacitor plates, then bound charge qb can be expressed as : − k ) (1) qb = qf(1 1 ) (2) qb = qi(1 −1 √k 1 ) + k (3) qb = qf(1 1 ) (4) qb = qf(1 + √k

Q12.A parallel-plate capacitor with plate area A has separation d between the plates. Two dielectric slabs of dielectric constant K1 and K2 of same area A2 and thickness d2 are inserted in the space between the plates. The capacitance of the capacitor will be given by : 2( K1+K2) (1) ε0 + + d K1+K2 K1 A ( 12 K1 K2 ) (2) ε0dA ( 21 K2 ) K1 (3) ε0 + K1+K2 + d 2( K1+K2) K2 ) A ( 12 K1 K2 ) (4) ε0dA ( 21