Practice Questions

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.If P × Q = Q × P , the angle between P and Q is θ(0°< θ < 360°). The value of θ 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 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 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.The average translational kinetic energy of 𝑁2 gas molecules at _________∘C becomes equal to the K . E . of an electron accelerated from rest through a potential difference of 0 . 1 volt . (Given 𝑘𝐵= 1 . 38 × 10-23 J K-1 (Fill the nearest integer).

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 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.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.In a spring gun having spring constant 100 N m−1 a small ball B of mass 100 g is put in its barrel (as shown in figure) by compressing the spring through 0. 05 m. There should be a box placed at a distance d on the ground so that the ball falls in it. If the ball leaves the gun horizontally at a height of 2 m above the ground. The value of d is m. (g = 10 m s−2)

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.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.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.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.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.The radius of a sphere is measured to be (7. 50 ± 0. 85) cm. Suppose the percentage error in its volume is x. The value of x, to the nearest x, is ___ .

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.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.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.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.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.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.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.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]