Practice Questions

Q24.A string of area of cross-section 4 mm2 and length 0. 5 is connected with a rigid body of mass 2 kg. The body is rotated in a vertical circular path of radius 0. 5 m. The body acquires a speed of 5 m s−1 at the bottom of the circular path. Strain produced in the string when the body is at the bottom of the circle is _____ ×10−5 . (Use Young's modulus 1011 N m−2 and g = 10 m s−2 )

Q24.Two coils require 20 minutes and 60 minutes respectively to produce same amount of heat energy when connected separately to the same source. If they are connected in parallel arrangement to the same source; the time required to produce same amount of heat by the combination of coils, will be _____ min.

Q24.The diameter of an air bubble which was initially 2 mm, rises steadily through a solution of density $1750 \mathrm{~kg} / \mathrm{m}^3$ at the rate of $0.35 \mathrm{~cm} / \mathrm{s}$. Coefficient of viscosity of the solution is ______ (Assume mass of the bubble to be negligible) (Answer in Poise to the nearest integer)

Q24.A unit scale is to be prepared whose length does not change with temperature and remains 20 cm, using a bimetallic strip made of brass and iron each of different length. The length of both components would change in such a way that difference between their lengths remains constant. If length of brass is 40 cm and length of iron will be _____ cm. 𝛼iron = 1 . 2 × 10-5 K-1 and 𝛼brass = 1 . 8 × 10-5 K-1.

Q24.A tunning fork of frequency 340 Hz resonates in the fundamental mode with an air column of length 125 cm in a cylindrical tube closed at one end. When water is slowly poured in it, the minimum height of water required for observing resonance once again is _____ cm. (Velocity of sound in air is 340 ms−1 )

Q24.The velocity of upper layer of water in a river is 36 km h-1. Shearing stress between horizontal layers of water is 10-3 N m-2. Depth of the river is _____ m. (Co-efficient of viscosity of water is 10-2 Pa s)

Q24.When a car is approaching the observer, the frequency of horn is 100 Hz. After passing the observer, it is 50 Hz. If the observer moves with the car, the frequency will be x3 Hz where x =_____ .

Q24.Two travelling waves of equal amplitudes and equal frequencies move in opposite directions along a string. They interfere to produce a stationary wave whose equation is given by y = (10 cos πx sin 2πtT ) cm . The amplitude of the particle at x = 34 cm will be _____ cm.

Q24.Nearly 10% of the power of a 110 W light bulb is converted to visible radiation. The change in average intensities of visible radiation, at a distance of 1 m from the bulb to a distance of 5 m is 𝑎× 10-2 W m-2. The value of '𝑎' will be

Q24.The position vector of 1 kg object is →r= (3ˆi −ˆj) m and its velocity →v= (3ˆj ˆk) its angular momentum is √x N m s, where x is

Q24.A spherical soap bubble of radius 3 cm is formed inside another spherical soap bubble of radius 6 cm. If the internal pressure of the smaller bubble of radius 3 cm in the above system is equal to the internal pressure of the another single soap bubble of radius r cm. The value of r is _____

Q24.Moment of Inertia (M.I.) of four bodies having same mass 𝑀 and radius 2𝑅 are as follows 𝐼1 = M.I. of solid sphere about its diameter 𝐼2 = M.I. of solid cylinder about its axis 𝐼3 = M.I. of solid circular disc about its diameter 𝐼4 = M.I. of thin circular ring about its diameter If 2𝐼2 + 𝐼3 + 𝐼4 = 𝑥𝐼1 then the value of 𝑥 will be _____ .

Q24.A mass 0. 9 kg, attached to a horizontal spring, executes SHM with an amplitude A1 . When this mass passes through its mean position, then a smaller mass of 124 g is placed over it and both masses move together with amplitude A2 . If the ratio A2A1 is α−1α , then the value of α will be _____ .

Q24.As per given figures, two springs of spring constants 𝐾 and 2 K are connected to mass m. If the period of oscillation in figure (a) is 3 s, then the period of oscillation in figure (b) will be √𝑥 s. The value of 𝑥 is _____ .

Q24.A geyser heats water flowing at a rate of 2. 0 kg per minute from 30°C to 70°C . If geyser operates on a gas burner, the rate of combustion of fuel will be _____ g min−1 . JEE Main 2022 (26 Jun Shift 2) JEE Main Previous Year Paper [Heat of combustion = 8 × 103 Jg−1 , Specific heat of water = 4. 2 Jg−1 ∘C−1 ]

Q24.A capacitor of capacitance 50 pF is charged by 100 V source. It is then connected to another uncharged identical capacitor. Electrostatic energy loss in the process is____ nJ .

Q24.Two waves executing simple harmonic motion travelling in the same direction with same amplitude and frequency are superimposed. The resultant amplitude is equal to the √3 times of amplitude of individual motions. The phase difference between the two motions is _____ (degree)

Q24.One mole of a monoatomic gas is mixed with three moles of a diatomic gas. The molecular specific heat of mixture at constant volume is α2 R J mol K−1 ; then the value of α will be _____ . (Assume that the given 4 diatomic gas has no vibrational mode.)

Q25.An ideal fluid of density 800 kg m−3 , flows smoothly through a bent pipe (as shown in figure) that tapers in cross-sectional area from a to a . The pressure difference between the wide and narrow sections of pipe is 2 4100 Pa . At wider section, the velocity of fluid is √x6 m s−1 for x = _____ . (Given g = 10 m s−2 )

Q25.Two resistors are connected in series across a battery as shown in figure. If a voltmeter of resistance 2000 Ω is used to measure the potential difference across 500 Ω resister, the reading of the voltmeter will be _____ V

Q25.A capacitor C1 of capacitance 5 μF is charged to a potential of 30 V using a battery. The battery is then removed and the charged capacitor is connected to an uncharged capacitor C2 of capacitance 10 μF as shown in figure. When the switch is closed charge flows between the capacitors. At equilibrium, the charge on the capacitor C2 is _____ μC.

Q25.Two parallel plate capacitors of capacity C and 3C are connected in parallel combination and charged to a potential difference 18 V . The battery is then disconnected and the space between the plates of the capacitor of capacity C is completely filled with a material of dielectric constant 9 . The final potential difference across the combination of capacitors will be _____ V .

Q25.At a certain temperature, the degrees of freedom per molecule for gas is 8 . The gas performs 150 J of work when it expands under constant pressure. The amount of heat absorbed by the gas will be _____ J.

Q25.The variation of applied potential and current flowing through a given wire is shown in figure. The length of wire is 31. 4 cm. The diameter of wire is measured as 2. 4 cm. The resistivity of the given wire is measured as x × 10−3 Ω cm. The value of x is _____ . [Take π = 3. 14 ]

Q25.A parallel plate capacitor is made up of stair like structure with a plate area A of each stair and that is x ε0 A , The connected with a wire of length b, as shown in the figure. The capacitance of the arrangement is b 15 value of x is _____ .