Practice Questions

Q4. Two bodies are projected from ground with same speeds 40 m s−1 at two different angles with respect to horizontal. The bodies were found to have same range. If one of the body was projected at an angle of 60° , with horizontal then sum of the maximum heights, attained by the two projectiles, is _____ m. (Given g = 10 m s−2 )

Q5. A body is dropped on ground from a height h1 and after hitting the ground, it rebounds to a height h2 . If the ratio of velocities of the body just before and after hitting ground is 4 , then percentage loss in kinetic energy of the body is x . The value of x is _____. 4

Q5. To maintain a speed of 80 km h−1 by a bus of mass 500 kg on a plane rough road for 4 km distance, the work done by the engine of the bus will be _____ kJ. [The coefficient of friction between tyre of bus and road is 0. 04 ]

Q5. A nucleus disintegrates into two smaller parts, which have their velocities in the ratio 3 : 2 . The ratio of their 1 nuclear sizes will be ( x3 ) 3 . The value of ‘ x’ is:

Q5. An object of mass m initially at rest on a smooth horizontal plane starts moving under the action of force F = 2 N . In the process of its linear motion, the angle θ (as shown in figure) between the direction of force and horizontal varies as θ = kx , where k is a constant and x is the distance covered by the object from its initial position. The expression of kinetic energy of the object will be E = nk sin θ . The value of n is ______.

Q5. The weight of a body at the surface of earth is 18 N. The weight of the body at an altitude of 3200 km above the earth's surface is (given, radius of earth 𝑅𝑒= 6400 km) (1) 9 . 8 N (2) 4 . 9 N (3) 19 . 6 N (4) 8 N

Q5. A block of mass 5 kg starting from rest pulled up on a smooth incline plane making an angle of 30° with horizontal with an effective acceleration of 1 m s−2 . The power delivered by the puling force at t = 10 s from the start is _____ W. [Use g = 10 m s−2 ] (Calculate the nearest integer value)

Q5. A force F = (5 + 3y2) acts on a particle in the y-direction, where F is newton and y is in meter. The work done by the force during a displacement from y = 2 m to y = 5 m is ______ J .

Q5. A body of mass 5 kg is moving with a momentum of 10 kg m s−1 . Now a force of 2 N acts on the body in the direction of its motion for 5 s. The increase in the Kinetic energy of the body is _____ J.

Q5. A particle of mass 100 g is projected at time t = 0 with a speed 20 m s–1 at an angle 45° to the horizontal as given in the figure. The magnitude of the angular momentum of the particle about the starting point at time t = 2 s is found to be √K kg m2 s−1 . The value of K is ______. (Take g = 10 m s−2 )

Q6. For rolling spherical shell, the ratio of rotational kinetic energy and total kinetic energy is x . The value of x is 5 _____.

Q6. A body of mass 1 kg collides head on elastically with a stationary body of mass 3 kg. After collision, the smaller body reverses its direction of motion and moves with a speed of 2 m s−1 . The initial speed of the smaller body before collision is ______ m s−1 . JEE Main 2023 (25 Jan Shift 2) JEE Main Previous Year Paper

Q6. A ball is dropped from a height of 20 m. If the coefficient of restitution for the collision between ball and floor is 0. 5 , after hitting the floor, the ball rebounds to a height of ______ m.

Q6. The momentum of a body is increased by 50% . The percentage increase in the kinetic energy of the body is_ _______%.

Q6. A 100 m long wire having cross-sectional area 6 . 25 × 10-4 m2 and Young's modulus is 1010 N m-2 is subjected to a load of 250 N, then the elongation in the wire will be : (1) 6 . 25 × 10-3 m (2) 4 × 10-4 m (3) 6 . 25 × 10-6 m (4) 4 × 10-3 m Q7. 1 g of a liquid is converted to vapour at 3 × 105 Pa pressure. If 10% of the heat supplied is used for increasing the volume by 1600 cm3 during this phase change, then the increase in internal energy in the process will be : (1) 4320 J (2) 432000 J (3) 4800 J (4) 4 . 32 × 108 J JEE Main 2023 (24 Jan Shift 1) JEE Main Previous Year Paper

Q6. A uniform solid cylinder with radius R and length L has moment of inertia I1 , about the axis of cylinder. A concentric solid cylinder of radius R′ = R2 and length L′ = L2 is carved out of the original cylinder. If I2 is the moment of inertia of the carved out portion of the cylinder then I1 = __________. I2 (Both I1 and I2 are about the axis of the cylinder)

Q6. A nucleus disintegrates into two nuclear parts, in such a way that ratio of their nuclear sizes is 1 : 21/3 . Their respective speed have a ratio of n : 1 . The value of n is_________

Q6. A 0. 4 kg mass takes 8 s to reach ground when dropped from a certain height P above surface of earth. The loss of potential energy in the last second of fall is ______ J. [Take g = 10 m s−2 ]

Q6. A hollow spherical ball of uniform density rolls up a curved surface with an initial velocity 3 m s−1 (as shown in figure). Maximum height with respect to the initial position covered by it will be _____ cm (take, g = 10 m s−2 ) JEE Main 2023 (08 Apr Shift 2) JEE Main Previous Year Paper

Q6. A body of mass 2 kg is initially at rest. It starts moving unidirectionally under the influence of a source of constant power P . Its displacement in 4 s is 31 α2√P m. The value of α will be ______. JEE Main 2023 (30 Jan Shift 2) JEE Main Previous Year Paper

Q6. A ring and a solid sphere rotating about an axis passing through their centres have same radii of gyration. The axis of rotation is perpendicular to plane of ring. The ratio of radius of ring to that of sphere is . The value √2x of x is _____.

Q7. If a solid sphere of mass 5 kg and a disc of mass 4 kg have the same radius, then the ratio of moment of inertia of the disc about a tangent in its plane to the moment of inertia of the sphere about its tangent will be x . The 7 value of x is ______.

Q7. Given below are two statements: Statement I: Acceleration due to earth's gravity decreases as you go 'up' or 'down' from earth's surface. JEE Main 2023 (24 Jan Shift 2) JEE Main Previous Year Paper Statement II: Acceleration due to earth's gravity is same at a height ' h' and depth ' d' from earth's surface, if h = d. In the light of above statements, choose the most appropriate answer form the options given below (1) Statement I is incorrect but statement II is correct (2) Both Statement I and Statement II are incorrect (3) Statement I is correct but statement II is incorrect (4) Both Statement I and II are correct

Q7. Two discs of same mass and different radii are made of different materials such that their thicknesses are 1 cm and 0. 5 cm respectively. The densities of materials are in the ratio 3 : 5 . The moment of inertia of these discs respectively about their diameters will be in the ratio of x . The value of x is ______. 6

Q7. ICM is moment of inertia of a circular disc about an axis (CM) passing through its center and perpendicular to the plane of disc. IAB is its moment of inertia about an axis AB perpendicular to plane and parallel to axis CM at a distance 2 R from center, where R is the radius of the disc. The ratio of IAB and ICM is x : 9. The value of x is 3 ______.