Practice Questions

Q21.Three particles P, Q and R are moving along the vectors A = ˆi +ˆj, B = ˆj + ˆk and C = −ˆi +ˆj, respectively. They strike on a point and start to move in different directions. Now particle P is moving normal to the plane → → → which contains vector A and B. Similarly particle Q is moving normal to the plane which contains vector A → and C. The angle between the direction of motion of P and Q is cos−1( √x1 ). Then the value of x is .

Q21.Suppose two planets (spherical in shape) of radii R and 2R, but mass M and 9M respectively have a centre to centre separation 8R as shown in the figure. A satellite of mass m is projected from the surface of the planet of mass M directly towards the centre of the second planet. The minimum speed v required for the satellite to GM reach the surface of the second planet is , then the value of a is R √a7 [Given : The two planets are fixed in their position]

Q21.A person is swimming with a speed of 10 m s−1 at an angle of 120° with the flow and reaches to a point directly opposite on the other side of the river. The speed of the flow is x m s−1. The value of x to the nearest integer is ______.

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 car is moving on a plane inclined at 30° to the horizontal with an acceleration of 10 m s−2 parallel to the plane upward. A bob is suspended by a string from the roof of the car. The angle in degrees which the string makes with the vertical is (Take g = 10 m s−2 )

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 )

Q21.A bullet of 10 g , moving with velocity v, collides head-on with the stationary bob of a pendulum and recoils with velocity 100 m s−1 . The length of the pendulum is 0. 5 m and mass of the bob is 1 kg. The minimum value of v in m s−1 , so that the pendulum describes a circle. (Assume the string to be inextensible and g = 10 m s−2 )

Q21.A particle is moving with constant acceleration 𝑎. Following graph shows 𝑣2 versus 𝑥 (displacement) plot. The acceleration of the particle is _________ m s-2 .

Q21.Two blocks ( m = 0. 5 kg and M = 4. 5 kg ) are arranged on a horizontal frictionless table as shown in the figure. The coefficient of static friction between the two blocks is 3 7 . Then the maximum horizontal force that can be applied on the larger block so that the blocks move together is N. (Round off to the Nearest Integer) [Take g as 9. 8 m s−2 ]

Q21.A force of F = (5y 20)ˆj y = 0 m to y = 10 m is ________ J .

Q22.A uniform chain of length 3 m and mass 3 kg overhangs a smooth table with 2 m laying on the table. If K is the kinetic energy of the chain in J as it completely slips off the table, then the value of K is (Take g = 10 m s−2)

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.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.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 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 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 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.Two bodies, a ring and a solid cylinder of same material are rolling down without slipping an inclined plane. The radii of the bodies are same. The ratio of velocity of the centre of mass at the bottom of the inclined plane of the ring to that of the cylinder is √x 2 . Then, the value of x is

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 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 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.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.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 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 = ________.