Practice Questions

Q22.A boy of mass 4 kg is standing on a piece of wood having mass 5 kg . If the coefficient of friction between the wood and the floor is 0. 5 , the maximum force that the boy can exert on the rope so that the piece of wood does not move from its place is _______ N . (Round off to the Nearest Integer) [Take g = 10 m s−2]

Q22.Consider a frame that is made up of two thin massless rods AB and AC as shown in the figure. A vertical → force P of magnitude 100 N is applied at point A of the frame. → Suppose the force is P resolved parallel to the arms AB and AC of the frame. The magnitude of the resolved component along the arm AC is xN . The value of x , to the nearest integer, is ________. [Given : sin(35°) = 0. 573, cos(35°) = 0. 819, sin(110°) = 0. 939, cos(110°) = −0. 342] JEE Main 2021 (16 Mar Shift 1) JEE Main Previous Year Paper

Q22.Wires W1 and W2 are made of same material having the breaking stress of 1. 25 × 109 N m−2. W1 and W2 have cross-sectional area of 8 × 10−7 m2 and 4 × 10−7 m2 , respectively. Masses of 20 kg and 10 kg hang from them as shown in the figure. The maximum mass that can be placed in the pan without breaking the wires is _____ kg (Use g = 10 m s−2)

Q22.A swimmer can swim with velocity of 12 km /h in still water. Water flowing in a river has velocity 6 km /h. The direction with respect to the direction of flow of river water he should swim in order to reach the point on the other bank just opposite to his starting point is ________ ° . (Round off to the Nearest Integer) (find the angle in degree) →

Q23.A parallel plate capacitor of capacitance 200𝜇F is connected to a battery of 200 V . A dielectric slab of dielectric constant 2 is now inserted into the space between plates of capacitor while the battery remain connected. The change in the electrostatic energy in the capacitor will be __________ J .

Q23.A ball with a speed of 9 m s-1 collides with another identical ball at rest. After the collision, the direction of each ball makes an angle of 30° with the original direction. If the ratio of velocities of the balls after the collision is 𝑥: 𝑦, then what is the value of 𝑥?

Q23.A body of mass (2M) splits into four masses {m, M −m, m, M −m}, which are rearranged to form a square as shown in the figure. The ratio of Mm for which, the gravitational potential energy of the system becomes maximum is x : 1. The value of x is ________.

Q23.A system consists of two types of gas molecules A and B having the same number density 2 × 1025 m−3 . The diameter of A and B are 10A and 5A respectively. They suffer collisions at room temperature. The ratio of average distance covered by the molecule A to that of B between two successive collisions is ___________ ×10−2

Q23.In the reported figure, two bodies 𝐴 and 𝐵 of masses 200 g and 800 g are attached with the system of springs. Springs are kept in a stretched position with some extension when the system is released. The horizontal surface is assumed to be frictionless. The angular frequency will be _______ rad s-1 when 𝑘= 20 N m-1.

Q23.In a certain thermodynamical process, the pressure of a gas depends on its volume as kV 3 . The work done when the temperature changes from 100 °C to 300 °C will be xnR where n denotes number of moles of a gas find x ;

Q23.The water is filled up to a height of 12 m in a tank having vertical sidewalls. A hole is made in one of the walls at a depth h below the water level. The value of h for which the emerging stream of water strikes the ground at the maximum range is _____ m .

Q23.The position of the centre of mass of a uniform semi-circular wire of radius R placed in x −y plane with its centre at the origin and the line joining its ends as x−axis is given by, (0, xRπ ). Then, the value of |x| is .

Q23.Two simple harmonic motions are represented by the equations x1 = 5 sin(2πt + π4 ) and 2πt + cos x2 = 5√2(sin 2πt). The amplitude of the second motion is _____ times the amplitude in the first motion.

Q23.In a uniform magnetic field, the magnetic needle has a magnetic moment 9. 85 × 10−2 A m−2 and moment of inertia 5 × 10−6 kg m2. If it performs 10 complete oscillations in 5 seconds then the magnitude of the magnetic field is ____ mT [Take π2 as 9. 85]

Q23.As shown in the figure, a block of mass √3 kg is kept on a horizontal rough surface of coefficient of friction 1 . The critical force to be applied on the vertical surface as shown at an angle 60° with horizontal such that 3√3 it does not move, will be 3x. The value of x will = 10 m s−2; sin 60°= √32 ; cos 60°= 21 ] [g

Q23.When a body slides down from rest along a smooth inclined plane making an angle of 30° with the horizontal, it takes time 𝑇. When the same body slides down from the rest along a rough inclined plane making the same angle and through the same distance, it takes time 𝛼𝑇, where 𝛼 is a constant greater than 1 . The co-efficient of 1 𝛼2 - 1 friction between the body and the rough plane is where 𝑥= __________ . √𝑥 𝛼2

Q23.When a rubber ball is taken to a depth of _______ m in deep sea, its volume decreases by 0. 5% (The bulk modulus of rubber = 9. 8 × 108 N m−2 Density of sea water = 103 kg m−3 , g = 9. 8 m s−2 )

Q23.The initial velocity vi required to project a body vertically upward from the surface of the earth to reach a height of 10R, where R is the radius of the earth, may be described in terms of escape velocity ve such that vi = × ve . The value of x will be √xy JEE Main 2021 (25 Feb Shift 2) JEE Main Previous Year Paper

Q23.A ball of mass 4 kg, moving with a velocity of 10 m s−1 , collides with a spring of length 8 m and force constant 100 N m−1 . The length of the compressed spring is x m. The value of x, to the nearest integer, is ___ .

Q23.A uniform metallic wire is elongated by 0. 04 m when subjected to a linear force F. The elongation, if its length and diameter is doubled and subjected to the same force will be _________ cm.

Q23.The disc of mass M with uniform surface mass density σ is shown in the figure. The center of mass of the quarter disc (the shaded area) is at the position ( xa3π , xa3π ) where x is _______ . (Round off to the Nearest Integer) [ a is an area as shown in the figure] JEE Main 2021 (17 Mar Shift 2) JEE Main Previous Year Paper

Q23.A heat engine operates between a cold reservoir at temperature T2 = 400 K and a hot reservoir at temperature T1 . It takes 300 J of heat from the hot reservoir and delivers 240 J of heat to the cold reservoir in a cycle. The minimum temperature of the hot reservoir has to be

Q23.The following bodies, (1) a ring (2) a disc (3) a solid cylinder (4) a solid sphere, of same mass m and radius R are allowed to roll down without slipping simultaneously from the top of the inclined plane. The body which will reach first at the bottom of the inclined plane is [Mark the body as per their respective numbering given in the question] JEE Main 2021 (17 Mar Shift 1) JEE Main Previous Year Paper

Q23.Consider a 20 kg uniform circular disk of radius 0. 2 m. It is pin supported at its center and is at rest initially. The disk is acted upon by a constant force F = 20 N through a massless string wrapped around its periphery as shown in the figure. Suppose the disk makes n number of revolutions to attain an angular speed of 50 rad s−1 . The value of n, to the nearest integer, is _______ . [Given : In one complete revolution, the disk rotates by 6. 28 rad]

Q23.The volume V of a given mass of monoatomic gas changes with temperature T according to the relation 2 V = KT 3 . The workdone when temperature changes by 90 K will be xR. The value of x is [ R universal gas constant ]