Practice Questions

Q21.If the projection of 2 ^𝑖+ 4 ^𝑗- 2 ^𝑘 on ^𝑖+ 2 ^𝑗+ 𝛼 ^𝑘 is zero. Then, the value of 𝛼 will be

Q21.A ball of mass 0. 5 kg is dropped from the height of 10 m . The height, at which the magnitude of velocity becomes equal to the magnitude of acceleration due to gravity, is _____ m. [Use g = 10 m s−2 ]

Q21.For 𝑧= 𝑎2𝑥3𝑦 12, where '𝑎' is a constant. If percentage error in measurement of '𝑥' and '𝑦' are 4%and 12%, respectively, then the percentage error for '𝑧' will be _____ % .

Q21.An object is projected in the air with initial velocity u at an angle θ. The projectile motion is such that the horizontal range R, is maximum. Another object is projected in the air with a horizontal range half of the range of first object. The initial velocity remains same in both the case. The value of the angle of projection, at which the second object is projected, will be _____ degree.

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.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.In an experiment to verify Newton's law of cooling. a graph is plotted between. the temperature difference (ΔT) of the water and surroundings and time as shown in figure. The initial temperature of water is taken as 80°C. The value of t2 as mentioned in the graph will be

Q22.A small spherical ball of radius 0. 1 mm and density 104 kg m−3 falls freely under gravity through a distance h before entering a tank of water. If, after entering the water the velocity of ball does not change and it JEE Main 2022 (29 Jun Shift 2) JEE Main Previous Year Paper continue to fall with same constant velocity inside water, then the value of h will be ____ m. (Given g = 10 m s−2 , viscosity of water = 1. 0 × 10−5 N‐s m−2 ).

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 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.The radius of gyration of a cylindrical rod about an axis of rotation perpendicular to its length and passing through the center will be _____ m . Given, the length of the rod is 10√3 m.

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 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 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 ball of mass 100 g is dropped from a height h = 10 cm on a platform fixed at the top of a vertical spring (as shown in figure). The ball stays on the platform and the platform is depressed by a distance h . The spring 2 constant is _____ N m−1 (Use g = 10 m s−2 )

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 )

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 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 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.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 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 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.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.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