Practice Questions

Q10.A certain charge Q is divided into two parts q and (Q −q). How should the charges Q and q be divided so that q and (Q −q) placed at a certain distance apart experience maximum electrostatic repulsion? (1) Q = 2q (2) Q = 2q (3) Q = 4q (4) Q = 3q JEE Main 2021 (20 Jul Shift 1) JEE Main Previous Year Paper

Q10.A student is performing the experiment of the resonance column. The diameter of the column tube is 6 cm. The frequency of the tuning fork is 504 Hz. Speed of the sound at the given temperature is 336 m s−1 . The zero of the meter scale coincides with the top end of the resonance column tube. The reading of the water level in the column when the first resonance occurs is: JEE Main 2021 (25 Feb Shift 1) JEE Main Previous Year Paper (1) 14. 8 cm (2) 18. 4 cm (3) 16. 6 cm (4) 13 cm

Q10.A bob of mass 𝑚 suspended by a thread of length ℓ undergoes simple harmonic oscillations with time period 1 𝑇. If the bob is immersed in a liquid that has density times that of the bob and the length of the thread is 4 1 𝑟𝑑 increased by of the original length, then the time period of the simple harmonic oscillations will be: 3 3 4 (1) 4𝑇 (2) 3𝑇 (3) 𝑇 (4) 3 2𝑇

Q10.Two ideal polyatomic gases at temperatures T1 and T2 are mixed so that there is no loss of energy. If F1 and F2, m1 and m2, n1 and n2 be the degrees of freedom, masses, number of molecules of the first and second gas respectively, the temperature of mixture of these two gases is: (1) n1 T 1+n2 T 2 (2) n1F1T1+n2F2T2 n1+n2 n1F1+n2F2 (3) n1 F 1 T 1+n2 F 2 T 2 (4) n1 F 1 T 1+n2 F 2 T 2 F 1+F2 n1+n2

Q10.Two small drops of mercury each of radius R coalesce to form a single large drop. The ratio of total surface energy before and after the change is (1) 2 13 : 1 (2) 1 : 2 31 (3) 2 : 1 (4) 1 : 2

Q10.A mass of 5 kg is connected to a spring. The potential energy curve of the simple harmonic motion executed by the system is shown in the figure. A simple pendulum of length 4 m has the same period of oscillation as the spring system. What is the value of acceleration due to gravity on the planet where these experiments are performed ? (1) 4 m s-2 (2) 8 m s-2 (3) 5 m s-2 (4) 10 m s-2

Q10.Two particles A and B having charges 20 μC and −5 μC respectively are held fixed with a separation of 5 cm At what position a third charged particle should be placed so that it does not experience a net electric force ? (1) At 5 cm from −5 μC on the right side (2) At 5 cm from 20 μC on the left side of system (3) At 1. 25 cm from −5 μC between two charges (4) At midpoint between two charges

Q10.A loop of flexible wire of irregular shape carrying current is placed in an external magnetic field. Identify the effect of the field on the wire. (1) Loop assumes circular shape with its plane normal to the field. (2) Loop assumes circular shape with its plane parallel to the field. (3) Wire gets stretched to become straight. (4) Shape of the loop remains unchanged.

Q10.A Copper (Cu) rod of length 25 cm and cross-sectional area 3 mm2 is joined with a similar Aluminium (Al) rod as shown in figure. Find the resistance of the combination between the ends A and B. (Take resistivity of Copper = 1. 7 × 10−8 Ωm , Resistivity of aluminium = 2. 6 × 10−8 Ωm ) (1) 2. 170 mΩ (2) 1. 420 mΩ (3) 0. 0858 mΩ (4) 0. 858 mΩ

Q10.In the given figure, the emf of the cell is 2. 2 V and if internal resistance is 0. 6 Ω . Calculate the power dissipated in the whole circuit: JEE Main 2021 (26 Aug Shift 1) JEE Main Previous Year Paper (1) 1.32 W (2) 4 .4 W (3) 0. 65 W (4) 2. 2 W

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

Q11.In the given figure, there is a circuit of potentiometer of length 𝐴𝐵= 10 m. The resistance per unit length is 0 . 1 Ω per cm. Across 𝐴𝐵, a battery of emf 𝐸 and internal resistance 𝑟 is connected. The maximum value of emf measured by this potentiometer is: JEE Main 2021 (25 Jul Shift 1) JEE Main Previous Year Paper (1) 5 V (2) 2 . 25 V (3) 6 V (4) 2 . 75 V

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.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.Which of the following graphs represent the behaviour of an ideal gas? Symbols have their usual meaning. (1) (2) (3) (4)

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.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.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.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. 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.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