Practice Questions

Q22.Consider a frame that is made up of two thin massless rods AB and AC as shown in the figure. A vertical → force P of magnitude 100 N is applied at point A of the frame. → Suppose the force is P resolved parallel to the arms AB and AC of the frame. The magnitude of the resolved component along the arm AC is xN . The value of x , to the nearest integer, is ________. [Given : sin(35°) = 0. 573, cos(35°) = 0. 819, sin(110°) = 0. 939, cos(110°) = −0. 342] JEE Main 2021 (16 Mar Shift 1) JEE Main Previous Year Paper

Q22.A block moving horizontally on a smooth surface with a speed of 40 m s−1 splits into two equal parts. If one of the parts moves at 60 m s−1 in the same direction, then the fractional change in the kinetic energy will be x : 4 where x = ________.

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.Two particles having masses 4 g and 16 g respectively are moving with equal kinetic energies. The ratio of the magnitudes of their linear momentum is n : 2 . The value of n will be ___.

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 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.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.A bullet of mass 0. 1 kg is fired on a wooden block to pierce through it, but it stops after moving a distance of 50 cm into it. If the velocity of the bullet before hitting the wood is 10 m s−1 and, it slows down with uniform deceleration, then the magnitude of effective retarding force on the bullet is x N. The value of x to the nearest integer is,

Q22.The angular speed of truck wheel is increased from 900 rpm to 2460 rpm in 26 seconds. The number of revolutions by the truck engine during this time is ______. (Assuming the acceleration to be uniform).

Q22.An inclined plane is bent in such a way that the vertical cross-section is given by 𝑦= 𝑥2 where 𝑦 is in vertical 4 and 𝑥 in horizontal direction. If the upper surface of this curved plane is rough with coefficient of friction 𝜇= 0 . 5, the maximum height in cm at which a stationary block will not slip downward is________cm . JEE Main 2021 (24 Feb Shift 1) JEE Main Previous Year Paper

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 stone of mass 20 g is projected from a rubber catapult of length 0. 1 m and area of cross section 10−6 m2 stretched by an amount 0. 04 m. The velocity of the projected stone is m s−1. (Young's modulus of rubber = 0. 5 × 109 N m−2 )

Q22.The coefficient of static friction between two blocks is 0. 5 and the table is smooth. The maximum horizontal force that can be applied to move the blocks together is _______ N (take g = 10 m s−2)

Q22.A swimmer can swim with velocity of 12 km /h in still water. Water flowing in a river has velocity 6 km /h. The direction with respect to the direction of flow of river water he should swim in order to reach the point on the other bank just opposite to his starting point is ________ ° . (Round off to the Nearest Integer) (find the angle in degree) →

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 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]

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.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.A ball with a speed of 9 m s-1 collides with another identical ball at rest. After the collision, the direction of each ball makes an angle of 30° with the original direction. If the ratio of velocities of the balls after the collision is 𝑥: 𝑦, then what is the value of 𝑥?

Q23.A body of mass (2M) splits into four masses {m, M −m, m, M −m}, which are rearranged to form a square as shown in the figure. The ratio of Mm for which, the gravitational potential energy of the system becomes maximum is x : 1. The value of x is ________.

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

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.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.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.The volume V of a given mass of monoatomic gas changes with temperature T according to the relation 2 V = KT 3 . The workdone when temperature changes by 90 K will be xR. The value of x is [ R universal gas constant ]