Practice Questions

Q23.A rod of mass M and length L is lying on a horizontal frictionless surface. A particle of mass m travelling along the surface hits at one end of the rod with a velocity u in a direction perpendicular to the rod. The collision is completely elastic. After collision, particle comes to rest. The ratio of masses ( Mm ) is x1 . The value of x will be

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 rotating with an angular speed of 600 rpm is uniformly accelerated to 1800 rpm in 10 sec. The number of rotations made in the process 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 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 ]

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 particle of mass 10 kg is placed at a point A. When the particle is slightly displaced to its right, it starts moving and reaches the point B. The speed of the particle at B is x m s−1 . (Take g = 10 m s−2) The value of x to the nearest integer is

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.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.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.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.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 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.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.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 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.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

Q24.The centre of a wheel rolling on a plane surface moves with a speed v0. A particle on the rim of the wheel at the same level as the centre will be moving at a speed √xv0. Then the value of x is .

Q24.A solid disc of radius a and mass m rolls down without slipping on an inclined plane making an angle θ with the horizontal. The acceleration of the disc will be 2 b g sin θ, where b is _______. (Round off to the Nearest Integer) ( g = acceleration due to gravity) ( θ = angle as shown in figure) JEE Main 2021 (16 Mar Shift 2) JEE Main Previous Year Paper

Q24.Consider an electrical circuit containing a two way switch S. Initially S is open and then T1 is connected to T2. As the current in R = 6 Ω attains a maximum value of steady-state level, T1 is disconnected from T2 and JEE Main 2021 (27 Jul Shift 1) JEE Main Previous Year Paper immediately connected to T3. Potential drop across r = 3 Ω resistor immediately after T1 is connected to T3 is ______V. (Round off to the Nearest Integer)

Q24.Two simple harmonic motion, are represented by the equations 3πt + √3 cos y1 = 10 sin(3πt + π3 ); y2 = 5(sin 3πt) Ratio of amplitude of y1 to y2 = x : 1 . The value of x is

Q24.A particle of mass 1 kg is hanging from a spring of force constant 100 N m−1. The mass is pulled slightly downward and released so that it executes free simple harmonic motion with time period T. The time when the kinetic energy and potential energy of the system will become equal, is T n . The value of n is ________. JEE Main 2021 (31 Aug Shift 1) JEE Main Previous Year Paper

Q24.A monoatomic gas of mass 4. 0 u is kept in an insulated container. The container is moving with velocity 30 m s−1 . If the container is suddenly stopped then a change in temperature of the gas ( R = gas constant) is 3Rx . Value of x is, → 3 4 N C−1 . The ratio of flux of reported field

Q24.A pendulum bob has a speed of 3 m s-1 at its lowest position. The pendulum is 50 cm long. The speed of bob, when the length makes an angle of 60° to the vertical will be 𝑔= 10 m s-2 ______ m s-1. JEE Main 2021 (25 Jul Shift 1) JEE Main Previous Year Paper

Q24.A rod CD of thermal resistance 10. 0 KW−1 is joined at the middle of an identical rod AB as shown in figure. The ends A, B and D are maintained at 200°C, 100°C and 125°C respectively. The heat current in CD is JEE Main 2021 (27 Aug Shift 1) JEE Main Previous Year Paper P W. The value of P is