Practice Questions

Q22.The potential energy (U) of a diatomic molecule is a function dependent on r (interatomic distance) as U = α −β −3 where, α and β are positive constants. The equilibrium distance between two atoms will be r10 r5 a , where a =______ . ( 2αβ ) b

Q22.Two persons A and B perform same amount of work in moving a body through a certain distance d with application of forces acting at angles 45° and 60° with the direction of displacement respectively. The ratio of force applied by person A to the force applied by person B is 1 . The value of x is _________. √x

Q22.An engine is attached to a wagon through a shock absorber of length 1 . 5 m . The system with a total mass of 40, 000 kg is moving with a speed of 72 km h-1 when the brakes are applied to bring it to rest. In the process of the system being brought to rest, the spring of the shock absorber gets compressed by 1 . 0 m. If 90% of energy of the wagon is lost due to friction, the spring constant is _________ × 105 N m-1 .

Q22.A sample of gas with 𝛾= 1 . 5 is taken through an adiabatic process in which the volume is compressed from 1200 cm3 to 300 cm3 . If the initial pressure is 200 kPa . The absolute value of the workdone by the gas JEE Main 2021 (31 Aug Shift 2) JEE Main Previous Year Paper in the process = ________ J .

Q22.A person standing on a spring balance inside a stationary lift measures 60 kg . The weight of that person if the lift descends with uniform downward acceleration of 1. 8 m s−2 will be N. [g = 10 m s−2]

Q22.A body having specific charge 8 μC g−1 is resting on a frictionless plane at a distance 10 cm from the wall (as shown in the figure). It starts moving towards the wall when a uniform electric field of 100 V m−1 is applied horizontally towards the wall. If the collision of the body with the wall is perfectly elastic, then the time period of the motion will be ____s.

Q22.A boy of mass 4 kg is standing on a piece of wood having mass 5 kg . If the coefficient of friction between the wood and the floor is 0. 5 , the maximum force that the boy can exert on the rope so that the piece of wood does not move from its place is _______ N . (Round off to the Nearest Integer) [Take g = 10 m s−2]

Q22.A small block slides down from the top of hemisphere of radius R = 3 m as shown in the figure. The height h at which the block will lose contact with the surface of the sphere is m. (Assume there is no friction between the block and the hemisphere)

Q22.The projectile motion of a particle of mass 5 g is shown in the figure. The initial velocity of the particle is 5√2 ms−1 and the air resistance is assumed to be negligible. The magnitude of the change in momentum between the points A and B is x × 10−2 kgms−1 . The value of x, to the nearest integer, is ___ .

Q22.A particle of mass 𝑚 is moving in time 𝑡 on a trajectory given by, →𝑟= 10𝛼𝑡2^i + 5𝛽𝑡- 5 ^j where 𝛼 and 𝛽 are dimensional constants. The angular momentum of the particle becomes the same as it was for 𝑡= 0 at time 𝑡= _____ seconds.

Q23.In a uniform magnetic field, the magnetic needle has a magnetic moment 9. 85 × 10−2 A m−2 and moment of inertia 5 × 10−6 kg m2. If it performs 10 complete oscillations in 5 seconds then the magnitude of the magnetic field is ____ mT [Take π2 as 9. 85]

Q23.The following bodies, (1) a ring (2) a disc (3) a solid cylinder (4) a solid sphere, of same mass m and radius R are allowed to roll down without slipping simultaneously from the top of the inclined plane. The body which will reach first at the bottom of the inclined plane is [Mark the body as per their respective numbering given in the question] JEE Main 2021 (17 Mar Shift 1) JEE Main Previous Year Paper

Q23.When a rubber ball is taken to a depth of _______ m in deep sea, its volume decreases by 0. 5% (The bulk modulus of rubber = 9. 8 × 108 N m−2 Density of sea water = 103 kg m−3 , g = 9. 8 m s−2 )

Q23.A body rotating with an angular speed of 600 rpm is uniformly accelerated to 1800 rpm in 10 sec. The number of rotations made in the process is

Q23.The position of the centre of mass of a uniform semi-circular wire of radius R placed in x −y plane with its centre at the origin and the line joining its ends as x−axis is given by, (0, xRπ ). Then, the value of |x| is .

Q23.A rod of mass M and length L is lying on a horizontal frictionless surface. A particle of mass m travelling along the surface hits at one end of the rod with a velocity u in a direction perpendicular to the rod. The collision is completely elastic. After collision, particle comes to rest. The ratio of masses ( Mm ) is x1 . The value of x will be

Q23.A heat engine operates between a cold reservoir at temperature T2 = 400 K and a hot reservoir at temperature T1 . It takes 300 J of heat from the hot reservoir and delivers 240 J of heat to the cold reservoir in a cycle. The minimum temperature of the hot reservoir has to be

Q23.As shown in the figure, a block of mass √3 kg is kept on a horizontal rough surface of coefficient of friction 1 . The critical force to be applied on the vertical surface as shown at an angle 60° with horizontal such that 3√3 it does not move, will be 3x. The value of x will = 10 m s−2; sin 60°= √32 ; cos 60°= 21 ] [g

Q23.The initial velocity vi required to project a body vertically upward from the surface of the earth to reach a height of 10R, where R is the radius of the earth, may be described in terms of escape velocity ve such that vi = × ve . The value of x will be √xy JEE Main 2021 (25 Feb Shift 2) JEE Main Previous Year Paper

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.

Q23.As shown in the figure, a particle of mass 10 kg is placed at a point A. When the particle is slightly displaced to its right, it starts moving and reaches the point B. The speed of the particle at B is x m s−1 . (Take g = 10 m s−2) The value of x to the nearest integer is

Q23.Consider a 20 kg uniform circular disk of radius 0. 2 m. It is pin supported at its center and is at rest initially. The disk is acted upon by a constant force F = 20 N through a massless string wrapped around its periphery as shown in the figure. Suppose the disk makes n number of revolutions to attain an angular speed of 50 rad s−1 . The value of n, to the nearest integer, is _______ . [Given : In one complete revolution, the disk rotates by 6. 28 rad]

Q23.In a certain thermodynamical process, the pressure of a gas depends on its volume as kV 3 . The work done when the temperature changes from 100 °C to 300 °C will be xnR where n denotes number of moles of a gas find x ;

Q23.A system consists of two types of gas molecules A and B having the same number density 2 × 1025 m−3 . The diameter of A and B are 10A and 5A respectively. They suffer collisions at room temperature. The ratio of average distance covered by the molecule A to that of B between two successive collisions is ___________ ×10−2

Q23.Consider a badminton racket with length scales as shown in the figure. JEE Main 2021 (26 Aug Shift 1) JEE Main Previous Year Paper If the mass of the linear and circular portions of the badminton racket are same ( M ) and the mass of the threads are negligible, the moment of inertia of the racket about an axis perpendicular to the handle and in the plane of the ring at, r distance from the end A of the handle will be ______ Mr2 . 2