Practice Questions

Q24.A particle of mass 1 kg is hanging from a spring of force constant 100 N m−1. The mass is pulled slightly downward and released so that it executes free simple harmonic motion with time period T. The time when the kinetic energy and potential energy of the system will become equal, is T n . The value of n is ________. JEE Main 2021 (31 Aug Shift 1) JEE Main Previous Year Paper

Q24.The radius in kilometer to which the present radius of earth (R = 6400 km) to be compressed so that the escape velocity is increased 10 time is _______.

Q24.A ball of mass 10 kg moving with a velocity 10√3 m s−1 along the x -axis, hits another ball of mass 20 kg which is at rest. After the collision, first ball comes to rest while the second ball disintegrates into two equal pieces. One piece starts moving along y -axis with a speed of 10 m s−1. The second piece starts moving at an angle of 30° with respect to the x -axis. The velocity of the ball moving at 30° with x -axis is x m s−1. The configuration of pieces after the collision is shown in the figure below. The value of x to the nearest integer is JEE Main 2021 (18 Mar Shift 1) JEE Main Previous Year Paper

Q24.A solid disc of radius a and mass m rolls down without slipping on an inclined plane making an angle θ with the horizontal. The acceleration of the disc will be 2 b g sin θ, where b is _______. (Round off to the Nearest Integer) ( g = acceleration due to gravity) ( θ = angle as shown in figure) JEE Main 2021 (16 Mar Shift 2) JEE Main Previous Year Paper

Q24.A rod CD of thermal resistance 10. 0 KW−1 is joined at the middle of an identical rod AB as shown in figure. The ends A, B and D are maintained at 200°C, 100°C and 125°C respectively. The heat current in CD is JEE Main 2021 (27 Aug Shift 1) JEE Main Previous Year Paper P W. The value of P is

Q24.Consider a water tank as shown in the figure. It's cross-sectional area is 0. 4 m2 . The tank has an opening B near the bottom whose cross-section area is 1 cm2 . A load of 24 kg is applied on the water at the top when the height of the water level is 40 cm above the bottom, the velocity of water coming out the opening B is v m s−1 . The value of v, to the nearest integer, is ___ .[Take the value of g to be 10 m s−2 ]

Q24.A resistor dissipates 192 J of energy in 1 s when a current of 4 A is passed through it. Now, when the current is doubled, the amount of thermal energy dissipated in 5 s is _____________ J .

Q24.A 2 kg steel rod of length 0 . 6 m is clamped on a table vertically at its lower end and is free to rotate in the vertical plane. The upper end is pushed so that the rod falls under gravity. Ignoring the friction due to clamping at its lower end, the speed of the free end of the rod when it passes through its lowest position is _______m s-1 . (Take 𝑔= 10 m s-2 )

Q24.A monoatomic gas of mass 4. 0 u is kept in an insulated container. The container is moving with velocity 30 m s−1 . If the container is suddenly stopped then a change in temperature of the gas ( R = gas constant) is 3Rx . Value of x is, → 3 4 N C−1 . The ratio of flux of reported field

Q24.A 16 Ω wire is bent to form a square loop. A 9 V supply having an internal resistance of 1 Ω is connected across one of its sides. The potential drop across the diagonals of the square loop is __________ ×10−1 V .

Q24.A particle executes S.H.M. with amplitude A and time period T . The displacement of the particle when its speed is half of maximum speed is √xA 2 . The value of x is

Q24.In the given figure, two wheels P and Q are connected by a belt B. The radius of P is three times that of Q. In the case of the same rotational kinetic energy, the ratio of rotational inertias ( I2I1 ) will be x : 1 . The value of x will be ______.

Q24.A pendulum bob has a speed of 3 m s-1 at its lowest position. The pendulum is 50 cm long. The speed of bob, when the length makes an angle of 60° to the vertical will be 𝑔= 10 m s-2 ______ m s-1. JEE Main 2021 (25 Jul Shift 1) JEE Main Previous Year Paper

Q24.A container is divided into two chambers by a partition. The volume of first chamber is 4. 5 litre and second chamber is 5. 5 litre. The first chamber contain 3. 0 moles of gas at pressure 2. 0 atm and second chamber contain 4. 0 moles of gas at pressure 3. 0 atm . After the partition is removed and the mixture attains equilibrium, then, the common equilibrium pressure existing in the mixture is x × 10−1 atm . Value of x (nearest integer) is

Q24.A soap bubble of the radius 3 cm is formed inside another soap bubble of radius, 6 cm . The radius of an equivalent soap bubble that has the same excess pressure as inside the smaller bubble with respect to the atmospheric pressure is____ cm.

Q24.Two waves are simultaneously passing through a string and their equations are : y1 = A1 sin k(x −vt), y2 = A2 sin k(x −vt + x0). Given amplitudes A1 = 12 mm and A2 = 5 mm, x0 = 3. 5 cm and wave number k = 6. 28 cm−1. The amplitude of resulting wave will be _____ mm.

Q24.The centre of a wheel rolling on a plane surface moves with a speed v0. A particle on the rim of the wheel at the same level as the centre will be moving at a speed √xv0. Then the value of x is .

Q24.Suppose you have taken a dilute solution of oleic acid in such a way that its concentration becomes 0. 01 cm3 of oleic acid per cm3 of the solution. Then you make a thin film of this solution (monomolecular thickness) of 1 area 4 cm2 by considering 100 spherical drops of radius ( 40π3 ) 3 × 10−3 cm. Then the thickness of oleic acid layer will be x × 10−14 m . Where x is ________ .

Q25.Two travelling waves produces a standing wave represented by equation. y = (1. 0 mm) cos[(1. 57 cm−1)x] sin[(78. 5 s−1) t]. The node closest to the origin in the region x > 0 will be at x =. . . . . . (in cm).

Q25.A common transistor radio set requires 12 V D . C . for its operation. The D . C . source is constructed by using a transformer and a rectifier circuit, which are operated at 220 V A . C . on standard domestic A . C . supply. The number of turns of secondary coil are 24, then the number of turns of primary are

Q25.Two circuits are shown in figure (a) and (b). At a frequency of _______ rad s−1 the average power dissipated in one cycle will be the same in both the circuits.

Q25.In the reported figure, heat energy absorbed by a system in going through a cyclic process is ______ πJ. JEE Main 2021 (20 Jul Shift 1) JEE Main Previous Year Paper

Q25.Two cars are approaching each other at an equal speed of 7. 2 km hr−1. When they see each other, both blow horns having a frequency of 676 Hz. The beat frequency heard by each driver will be _______ Hz. [Velocity of sound in air is 340 m s−1.

Q25.A long solenoid with 1000 turns m-1 has a core material with relative permeability 500 and volume 103 cm3 . If the core material is replaced by another material having relative permeability of 750 with same volume maintaining same current of 0 . 75 A in the solenoid, the fractional change in the magnetic moment of 𝑥 the core would be approximately . Find the value of 𝑥. 499

Q25.A wire having a linear mass density 9. 0 × 10−4 kg m−1 is stretched between two rigid supports with a tension of 900 N. The wire resonates at a frequency of 500 Hz. The next higher frequency at which the same wire resonates is 550 Hz. The length of the wire is ___________ m.