Practice Questions

Q23.Two simple harmonic motions are represented by the equations x1 = 5 sin(2πt + π4 ) and 2πt + cos x2 = 5√2(sin 2πt). The amplitude of the second motion is _____ times the amplitude in the first motion.

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 hydraulic press can lift 100 kg when a mass 𝑚 is placed on the smaller piston. It can lift kg when the diameter of the larger piston is increased by 4 times and that of the smaller piston is decreased by 4 times keeping the same mass 𝑚 on the smaller piston.

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.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 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.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 ________ .

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.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.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.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 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.One mole of an ideal gas at 27 °C is taken from A to B as shown in the given PV indicator diagram. The work done by the system will be _______ ×10−1 J. [Given, R = 8. 3 J mole−1 K, ln 2 = 0. 6931] (Round off to the nearest integer) JEE Main 2021 (20 Jul Shift 2) JEE Main Previous Year Paper (Round off to the nearest integer)

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 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.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 circular disc reaches from top to bottom of an inclined plane of length L. When it slips down the plane, it . The value of x will be takes time t1 . When it rolls down the plane, it takes time t2 . The value of t2t1 is √3x

Q24.Two simple harmonic motion, are represented by the equations 3πt + √3 cos y1 = 10 sin(3πt + π3 ); y2 = 5(sin 3πt) Ratio of amplitude of y1 to y2 = x : 1 . The value of x is

Q24.A reversible heat engine converts one-fourth of the heat input into work. When the temperature of the sink is reduced by 52 K, its efficiency is doubled. The temperature in Kelvin of the source will be ___ .

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.

Q25.The area of cross-section of a railway track is 0. 01 m2. The temperature variation is 10 °C. Coefficient of linear expansion of material of track is 10−5 ∘C−1. The energy stored per meter in the track is J m−1. (Young's modulus of material of track is 1011 N m−2 )

Q25.Two cars X and Y are approaching each other with velocities 36 km h−1 and 72 km h−1 respectively. The frequency of a whistle sound as emitted by a passenger in car X, heard by the passenger in car Y is 1320 Hz. If the velocity of sound in air is 340 ms−1, the actual frequency of the whistle sound produced is ________ Hz.

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.The width of one of the two slits in a Young's double slit experiment is three times the other slit. If the amplitude of the light coming from a slit is proportional to the slit-width, the ratio of minimum to maximum intensity in the interference pattern is 𝑥: 4 where 𝑥 is _______ .

Q25.In the figure given, the electric current flowing through the 5 kΩ resistor is x mA . The value of x to the nearest integer is ________.