Practice Questions

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 .

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 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.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.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.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.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 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.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 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.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.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.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.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 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 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.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.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

Q23.The depth below the surface of sea to which a rubber ball be taken so as to decrease its volume by 0 . 02% is _____ m. (Take density of sea water = 103 kg m-3, Bulk modulus of rubber = 9 × 108 N m-2, and 𝑔= 10 m s-2)

Q23. A hydraulic press containing water has two arms with diameters as mentioned in the figure. A force of 10 N is applied on the surface of water in the thinner arm. The force required to be applied on the surface of water in the thicker arm to maintain equilibrium of water is _____N.

Q23.A circular disc reaches from top to bottom of an inclined plane of length l. When it slips down the plane, if α is _________ takes t s. When it rolls down the plane then it takes ( α2 )1/2t s, where

Q23.The density and breaking stress of a wire are 6 × 104 kg/m3 and 1.2 × 108 N/m2 respectively. The wire is 1 rd suspended from a rigid support on a planet where acceleration due to gravity is of the value on the surface 3 of earth. The maximum length of the wire with breaking is _____ m (take, g = 10 m/s2 ).

Q23.Two blocks of mass 2 kg and 4 kg are connected by a metal wire going over a smooth pulley as shown in figure. The radius of wire is 4 . 0 × 10-5 m and Young's modulus of the metal is 2 . 0 × 1011 N m-2. The 𝛼 is _____. [Use 𝑔= 10 m s-2) longitudinal strain developed in the wire is 𝛼𝜋.1 The value of 𝛼 is