Practice Questions

Q21.If P × Q = Q × P , the angle between P and Q is θ(0°< θ < 360°). The value of θ will be ___ ° .

Q21.Two solids A and B of mass 1 kg and 2 kg respectively are moving with equal linear momentum. The ratio of their kinetic energies (K. E. )A : (K. E. )B will be A1 , so the value of A will be _________.

Q21.If the velocity of a body related to displacement x is given by v = √5000 + 24x m s−1, then the acceleration of the body is _________ m s−2.

Q21.A body of mass 2 kg moving with a speed of 4 m s-1 makes an elastic collision with another body at rest and continues to move in the original direction but with one fourth of its initial speed. The speed of the two body centre of mass is $x/10$. Find the value of x.

Q21.A body of mass 2 kg moves under a force of (2ˆi + 3ˆj + 5ˆk)N It starts from rest and was at the origin initially. After 4 s, its new coordinates are (8, b, 20). The value of b is ______. (Round off to the Nearest Integer)

Q21.A body of mass m is launched up on a rough inclined plane making an angle of 30° with the horizontal. The coefficient of friction between the body and plane is √x if the time of ascent is half of the time of descent. The 5 value of x is

Q21.A body of mass 1 kg rests on a horizontal floor with which it has a coefficient of static friction 1 . It is √3 desired to make the body move by applying the minimum possible force F N . The value of F will be _______. (Round off to the Nearest Integer) [Take g = 10 m s−2 ]

Q21.The coefficient of static friction between a wooden block of mass 0 . 5 kg and a vertical rough wall is 0 . 2 . The magnitude of the horizontal force that should be applied on the block to keep it adhere to the wall will be______N. 𝑔= 10 m s-2

Q21.A swimmer wants to cross a river from point A to point B. Line AB makes an angle of 30° with the flow of the river. The magnitude of the velocity of the swimmer is the same as that of the river. The angle θ with the line AB should be _______ °, so that the swimmer reaches point B. JEE Main 2021 (27 Jul Shift 2) JEE Main Previous Year Paper

Q21.Two spherical balls having equal masses with radius of 5 cm each are thrown upwards along the same vertical direction at an interval of 3 s with the same initial velocity of 35 m s−1 , then these balls collide at a height of _____ m , (take g = 10 m s−2 )

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.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.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 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.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.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 solid disc of radius 20 cm and mass 10 kg is rotating with an angular velocity of 600 rpm, about an axis normal to its circular plane and passing through its centre of mass. The retarding torque required to bring the disc at rest in 10 s is _________ π × 10−1 N m

Q22.Wires W1 and W2 are made of same material having the breaking stress of 1. 25 × 109 N m−2. W1 and W2 have cross-sectional area of 8 × 10−7 m2 and 4 × 10−7 m2 , respectively. Masses of 20 kg and 10 kg hang from them as shown in the figure. The maximum mass that can be placed in the pan without breaking the wires is _____ kg (Use 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 uniform thin bar of mass 6 kg and length 2. 4 meter is bent to make an equilateral hexagon. The moment of inertia about an axis passing through the centre of mass and perpendicular to the plane of hexagon is ___________ ×10−1 kg m2.

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.

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.Three students S1, S2 and S3 perform an experiment for determining the acceleration due to gravity (g) using a simple pendulum. They use different lengths of pendulum and record time for different number of oscillations. The observations are as shown in the table. Student No. Length of pendulum Number of oscillations Total time for Time (cm) (n) n oscillations period JEE Main 2021 (22 Jul Shift 1) JEE Main Previous Year Paper (s) 1. 64. 0 8 128. 0 16. 0 2. 64. 0 4 64. 0 16. 0 3. 20. 0 4 36. 0 9. 0 (Least count of length = 0. 1 m , least count for time = 0. 1 s ) If E1, E2 and E3 are the percentage errors in g for students 1, 2 and 3 , respectively, then the minimum percentage error is obtained by student no .

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.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)