Practice Questions

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 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.A ball rolls off the top of a stairway with horizontal velocity u. The steps are 0. 1 m high and 0. 1 m wide. The minimum velocity u with which that ball just hits the step 5 of the stairway will be √x m s−1 , where x = _______ [use g = 10 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 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.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 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.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.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.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.The identical spheres each of mass 2𝑀 are placed at the corners of a right angled triangle with mutually perpendicular sides equal to 4 m each. Taking point of intersection of these two sides as origin, the 4√2 magnitude of position vector of the centre of mass of the system is 𝑥, where the value of 𝑥 is ________.

Q22.A uniform rod 𝐴𝐵 of mass 2 kg and Length 30 cm at rest on a smooth horizontal surface. An impulse of force 0 . 2 N s is applied to end B. The time taken by the rod to turn through at right angles will be 𝜋 s, x where 𝑥= ____.

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 hollow sphere is rolling on a plane surface about its axis of symmetry. The ratio of rotational kinetic energy to its total kinetic energy is x . The value of x is _____ . 5

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 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.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.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.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.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 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.A solid sphere and a hollow cylinder roll up without slipping on same inclined plane with same initial speed v. The sphere and the cylinder reaches upto maximum heights h1 and h2 , respectively, above the initial level. The ratio h1 : h2 is 10n . The value of n is______. JEE Main 2024 (04 Apr Shift 1) JEE Main Previous Year Paper

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 .

Q23.In a test experiment on a model aeroplane in wind tunnel, the flow speeds on the upper and lower surfaces of the wings are 70 m s−1 and 65 m s−1 respectively. If the wing area is 2 m2 , the lift of the wing is _______ N . (Given density of air = 1. 2 kg m−3 )

Q23.Mercury is filled in a tube of radius 2 cm up to a height of 30 cm. The force exerted by mercury on the bottom of the tube is _____ N. (Given, atmospheric pressure = 105Nm−2 , density of mercury = 1.36 × 104 kg m− 3, g = 10 m s−2, π = 227 )