Practice Questions

Q21.A vector has magnitude same as that of 𝐴= 3 ^j + 4 ^j and is parallel to 𝐵= 4 ^i + 3 ^j. The 𝑥 and 𝑦 components of this vector in first quadrant are 𝑥 and 3 respectively where x = ____.

Q21.Two forces ¯F1 and ¯F2 are acting on a body. One force has magnitude thrice that of the other force and the 1 ) resultant of the two forces is equal to the force of larger magnitude. The angle between →F1 and →F2 is cos−1 ( n . The value of |n| is _____.

Q21.A bus moving along a straight highway with speed of 72 km/h is brought to halt within 4s after applying the brakes. The distance travelled by the bus during this time (Assume the retardation is uniform) is _____m.

Q21.The displacement and the increase in the velocity of a moving particle in the time interval of t to (t + 1) s are 125 m and 50 m s−1 , respectively. The distance travelled by the particle in (t + 2)th s is ___________ m .

Q21.A particle initially at rest starts moving from reference point 𝑥= 0 along 𝑥-axis, with velocity 𝑣 that varies as 𝑣= 4√𝑥 m s-1. The acceleration of the particle is _____ m s-2.

Q21.Two identical spheres each of mass 2 kg and radius 50 cm are fixed at the ends of a light rod so that the separation between the centers is 150 cm. Then, moment of inertia of the system about an axis perpendicular to the rod and passing through its middle point is 𝑥 kg m2, where the value of 𝑥 is 20

Q21.A particle is moving in a circle of radius 50 cm in such a way that at any instant the normal and tangential components of its acceleration are equal. If its speed at t = 0 is 4 m s−1 , the time taken to complete the first revolution will be 1 [1 −e−2π] s, where α =______. α

Q21.A particle starts from origin at t = 0 with a velocity 5ˆi m s−1 and moves in x −y plane under action of a force which produces a constant acceleration of + m s−2 . If the x-coordinate of the particle at that instant is (3ˆi 2ˆj) 84 m, then the speed of the particle at this time is √α m s−1 . The value of α is _______.

Q21.A particle moves in a straight line so that its displacement x at any time t is given by x2 = 1 + t2 . Its acceleration at any time t is x−n where n = ___________

Q22.A body of mass 5 kg moving with a uniform speed 3√2 m s−1 in X −Y plane along the line y = x + 4. The angular momentum of the particle about the origin will be _______ kg m2 s−1 .

Q22.A string is wrapped around the rim of a wheel of moment of inertia 0.40kgm2 and radius 10 cm. The wheel is free to rotate about its axis. Initially the wheel is at rest. The string is now pulled by a force of 40 N. The angular velocity of the wheel after 10 s is xrad/s, where x is _______

Q22.A solid circular disc of mass 50 kg rolls along a horizontal floor so that its center of mass has a speed of 0 . 4 m s-1. The absolute value of work done on the disc to stop it is ______ J.

Q22.Three balls of masses 2 kg, 4 kg and 6 kg respectively are arranged at centre of the edges of an equilateral triangle of side 2 m. The moment of intertia of the system about an axis through the centroid and perpendicular to the plane of triangle, will be _______ kgm2 .

Q22.A circular table is rotating with an angular velocity of ωrad/s about its axis (see figure). There is a smooth groove along a radial direction on the table. A steel ball is gently placed at a distance of 1 m on the groove. All the surfaces are smooth. If the radius of the table is 3 m , the radial velocity of the ball w.r.t. the table at the time ball leaves the table is x√2ωm/s, where the value of x is _____.

Q22.In a system two particles of masses m1 = 3 kg and m2 = 2 kg are placed at certain distance from each other. The particle of mass m1 is moved towards the center of mass of the system through a distance 2 cm . In order to keep the center of mass of the system at the original position, the particle of mass m2 should move towards the center of mass by the distance _____ cm .

Q22.Three blocks M1, M2, M3 having masses 4 kg, 6 kg and 10 kg respectively are hanging from a smooth pully using rope 1,2 and 3 as shown in figure. The tension in the rope 1, T1 when they are moving upward with JEE Main 2024 (05 Apr Shift 1) JEE Main Previous Year Paper acceleration of 2 ms−2 is _____ N ( if g = 10 m/s2 ).

Q22.A body of mass 𝑚 is projected with a speed 𝑢 making an angle of 45o with the ground. The angular √2𝑚𝑢3 momentum of the body about the point of projection, at the highest point is expressed as 𝑋𝑔. The value of 𝑋 is_______.

Q22.A ring and a solid sphere roll down the same inclined plane without slipping. They start from rest. The radii of x is ______. both bodies are identical and the ratio of their kinetic energies is 7x, where

Q22.Four particles, each of mass 1 kg are placed at four corners of a square of side 2 m . The moment of inertia of the system about an axis perpendicular to its plane and passing through one of its vertex is ______ kg m2 .

Q22.A uniform thin metal plate of mass 10 kg with dimensions is shown. The ratio of x and y coordinates of center of mass of plate in n . The value of n is ________ 9

Q22.If the radius of earth is reduced to three-fourth of its present value without change in its mass then value of duration of the day of earth will be ______ hours 30 minutes.

Q22.A cylinder is rolling down on an inclined plane of inclination 60°. Its acceleration during rolling down will be x m s−2 , where x = _______(use g = 10 m s−2 ). √3

Q22.Consider a disc of mass 5 kg, radius 2 m , rotating with angular velocity of 10 rad s−1 about an axis perpendicular to the plane of rotation. An identical disc is kept gently over the rotating disc along the same axis. The energy dissipated so that both the discs continue to rotate together without slipping is _________ J.

Q22.Two discs of moment of inertia 𝐼1 = 4 kg m2 and 𝐼2 = 2 kg m2 about their central axes & normal to their planes, rotating with angular speeds 10 rad s-1 & 4 rad s-1 respectively are brought into contact face to face with their axe of rotation coincident. The loss in kinetic energy of the system in the process is _________J .

Q22.A force (3x2 + 2x −5)N displaces a body from x = 2 m to x = 4 m . Work done by this force is ________ J .