Practice Questions

Q22.A block of mass '𝑚' (as shown in figure) moving with kinetic energy 𝐸 compresses a spring through a distance 25 cm when, its speed is halved. The value of spring constant of used spring will be 𝑛𝐸 N m-1 for 𝑛= _____.

Q22.A uniform disc with mass M = 4 kg and radius R = 10 cm is mounted on a fixed horizontal axle as shown in figure. A block with mass m = 2 kg hangs from a massless cord that is wrapped around the rim of the disc. During the fall of the block, the cord does not slip and there is no friction at the axle. The tension in the cord is _____ N . (Take g = 10 ms−2 ) JEE Main 2022 (28 Jun Shift 2) JEE Main Previous Year Paper

Q22.A rolling wheel of 12 kg is on an inclined plane at position P and connected to a mass of 3 kg through a string of fixed length and pulley as shown in figure. Consider PR as friction free surface. The velocity of centre of mass of the wheel when it reaches at the bottom Q of the inclined plane PQ will be 1 √xgh m s−1 . The value of x (rounded off to the nearest integer) is _____. 2

Q22.A metal wire of length 0 . 5 m and cross-sectional area 10-4 m2 has breaking stress 5 × 108 N m-2. A block of 10 kg is attached at one end of the string and is rotating in a horizontal circle. The maximum linear velocity of block will be _____ m s-1.

Q22.A ball is thrown vertically upwards with a velocity of 19. 6 m s−1 from the top of a tower. The ball strikes the ground after 6 s. The height from the ground up to which the ball can rise will be ( k5 ) m. The value of k is _____ (use g = 9. 8 m s−2 )

Q22.A force on an object of mass 100 g is 10 ^i + 5 ^j N. The position of that object at 𝑡= 2 s is 𝑎 ^i + 𝑏 ^j m after 𝑎 starting from rest. The value of will be _____ . 𝑏

Q22.A curved in a level road has a radius 75 m. The maximum speed of a car turning this curved road can be 30 m s-1 without skidding. If radius of curved road is changed to 48 m and the coefficient of friction between the tyres and the road remains same, then maximum allowed speed would be _____ m s-1.

Q22.A fighter jet is flying horizontally at a certain altitude with a speed of 200 m s−1 . When it passes directly overhead an anti-aircraft gun, a bullet is fired from the gun, at an angle θ with the horizontal, to hit the jet. If the bullet speed is 400 m s−1 , the value of θ will be _____ °.

Q22.If the acceleration due to gravity experienced by a point mass at a height h above the surface of earth is same as that of the acceleration due to gravity at a depth αh(h ≪Re) ) from the earth surface. The value of α will be _____ . (use Re = 6400 km)

Q22.A system to 10 balls each of mass 2 kg are connected via massless and unstretchable string. The system is allowed to slip over the edge of a smooth table as shown in figure. Tension on the string between the 7th and 8th ball is _____ N when 6th ball just leaves the table.

Q22.The area of cross-section of a large tank is 0. 5 m2 . It has a narrow opening near the bottom having area of cross-section 1 cm2 . A load of 25 kg is applied on the water at the top in the tank. Neglecting the speed of water in the tank, the velocity of the water, coming out of the opening at the time when the height of water level in the tank is 40 cm above the bottom, will be _____ cm s−1 . [Take g = 10 m s−2 ]

Q22.If the initial velocity in horizontal direction of a projectile is unit vector ˆi and the equation of trajectory is y = 5x(1 −x). The y component vector of the initial velocity is _____ ˆj (Take g = 10 m s−2 )

Q22.A pulley of radius 1. 5 m is rotated about its axis by a force F = (12t −3t2) N applied tangentially (while t is measured in seconds). If moment of inertia of the pulley about its axis of rotation is 4. 5 kg m2 , the number of rotations made by the pulley before its direction of motion is reversed, will be K . The value of K is _____ . π

Q22.Four forces are acting at a point 𝑃 in equilibrium as shown in figure. The ratio of force 𝐹1 to 𝐹2 is 1: 𝑥 where 𝑥= _____ . JEE Main 2022 (25 Jul Shift 1) JEE Main Previous Year Paper

Q22.A pendulum is suspended by a string of length 250 cm. The mass of the bob of the pendulum is 200 g . The bob is pulled aside until the string is at 60° with vertical as shown in the figure. After releasing the bob, the maximum velocity attained by the bob will be _____ m s−1 . (if g = 10 m s−2 ) JEE Main 2022 (28 Jun Shift 1) JEE Main Previous Year Paper

Q22.Three identical spheres each of mass M are placed at the corners of a right angled triangle with mutually perpendicular sides equal to 3 m each. Taking point of intersection of mutually perpendicular sides as origin, the magnitude of position vector of centre of mass of the system will be √x m. The value of x is JEE Main 2022 (25 Jul Shift 2) JEE Main Previous Year Paper

Q22.A solid cylinder length is suspended symmetrically through two massless strings, as shown in the figure. The distance from the initial rest position, the cylinder should be unbinding the strings to achieve a speed of 4 m s−1 , is _____ cm. (take g = 10 m s−2 )

Q23.In an experiment to determine the Young's modulus, steel wires of five different lengths ( 1, 2, 3, 4 and 5 ) but of same cross-section (2 mm2) were taken and curves between extension and load were obtained. The slope JEE Main 2022 (27 Jul Shift 2) JEE Main Previous Year Paper (extension/load) of the curves were plotted with the wire length and the following graph is obtained. If the Young's modulus of given steel wires is x × 1011N m−2 , then the value of x is _____ .

Q23.A uniform heavy rod of mass 20 kg. Cross sectional area 0 . 4 m2 and length 20 m is hanging from a fixed support. Neglecting the lateral contraction, the elongation in the rod due to its own weight is 𝑥× 10-9 m. The value of 𝑥 is _____ . (Given. Young's modulus 𝑌= 2 × 1011Nm-2 and 𝑔= 10 m s-2 )

Q23.Four identical discs each of mass '𝑀' and diameter '𝑎' are arranged in a small plane as shown in figure. If the 𝑥 will be _____ . moment of inertia of the system about 𝑂𝑂' is 4𝑀𝑎2.𝑥 Then, the value of

Q23.A metre scale is balanced on a knife edge at its centre. When two coins, each of mass 10 g are put one on the top of the other at the 10. 0 cm mark the scale is found to be balanced at 40. 0 cm mark. The mass of the metre scale is found to be x × 10−2 kg. The value of x is _____ . Q24. 0. 056 kg of Nitrogen is enclosed in a vessel at a temperature of 127°C. The amount of heat required to double the speed of its molecules is_____ kcal. (Take R = 2 cal mole −1 K−1 )

Q23.The elongation of a wire on the surface of the earth is 10−4 m. The same wire of same dimensions is elongated by 6 × 10−5 m on another planet. The acceleration due to gravity on the planet will be _____ m s−2 . (Take acceleration due to gravity on the surface of earth = 10 m s−2 )

Q23.The distance of centre of mass from end A of a one dimensional rod (AB) having mass density ρ = kg m−1 and length L (in meter) is 3Lα m. The value of α is _____ (where x is the distance ρ0(1 −x2L2 ) form end A ) JEE Main 2022 (28 Jul Shift 2) JEE Main Previous Year Paper

Q23.A body is performing simple harmonic with an amplitude of 10 cm. The velocity of the body was tripled by air Jet when it is at 5 cm from its mean position. The new amplitude of vibration is √x cm. The value of x is _____ .

Q23.The pressure P1 and density d1 of diatomic gas (γ = 75 ) changes suddenly to P2(> P1) and d2 respectively during an adiabatic process. The temperature of the gas increases and becomes____times of its initial temperature. (given d2 = 32) d1