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## Numerical

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The distance of centre of mass from end A of a one dimensional rod (AB) having mass density $$\rho=\rho_{0}\left(1-\frac... JEE Main 2022 (Online) 28th July Evening Shift A batsman hits back a ball of mass 0.4 kg straight in the direction of the bowler without changing its initial speed of ... JEE Main 2022 (Online) 26th June Evening Shift A rolling wheel of 12 kg is on an inclined plane at position P and connected to a mass of 3 kg through a string of fixed... JEE Main 2022 (Online) 27th June Evening Shift A man of 60 kg is running on the road and suddenly jumps into a stationary trolly car of mass 120 kg. Then, the trolly c... JEE Main 2022 (Online) 28th June Morning Shift The position vector of 1 kg object is$$\overrightarrow r = \left( {3\widehat i - \widehat j} \right)m$$and its veloci... JEE Main 2022 (Online) 28th June Morning Shift A bullet of 10 g, moving with velocity v, collides head-on with the stationary bob of a pendulum and recoils with veloci... JEE Main 2021 (Online) 27th August Evening Shift Consider a badminton racket with length scales as shown in the figure.If the mass of the linear and circular portions of... JEE Main 2021 (Online) 26th August Morning Shift A body of mass 2 kg moving with a speed of 4 m/s. makes an elastic collision with another body at rest and continues to ... JEE Main 2021 (Online) 25th July Morning Shift The position of the centre of mass of a uniform semi-circular wire of radius 'R' placed in x-y plane with its centre at ... JEE Main 2021 (Online) 22th July Evening Shift A rod of mass M and length L is lying on a horizontal frictionless surface. A particle of mass 'm' travelling along the ... JEE Main 2021 (Online) 20th July Morning Shift The projectile motion of a particle of mass 5 g is shown in the figure.The initial velocity of the particle is$$5\sqrt ...
JEE Main 2021 (Online) 18th March Evening Shift
A ball of mass 10 kg moving with a velocity 10$$\sqrt 3$$ m/s along the x-axis, hits another ball of mass 20 kg which i...
JEE Main 2021 (Online) 18th March Morning Shift
The disc of mass M with uniform surface mass density $$\sigma$$ is shown in the figure. The centre of mass of the quarte...
JEE Main 2021 (Online) 17th March Evening Shift
A force $$\overrightarrow F$$ = $${4\widehat i + 3t\widehat j + 4\widehat k}$$ is applied on an intersection point of x...
JEE Main 2021 (Online) 16th March Evening Shift
A ball of mass 10 kg moving with a velocity $$10\sqrt 3$$ m s$$-$$1 along X-axis, hits another ball of mass 20 kg which...
JEE Main 2021 (Online) 16th March Morning Shift
Two particles having masses 4 g and 16 g respectively are moving with equal kinetic energies. The ratio of the magnitude...
JEE Main 2021 (Online) 25th February Evening Shift
Two solids A and B of mass 1 kg and 2 kg respectively are moving with equal linear momentum. The ratio of their kinetic ...
JEE Main 2021 (Online) 24th February Evening Slot
Two bodies of the same mass are moving with the same speed, but in different directions in a plane. They have a complete...
JEE Main 2020 (Online) 6th September Morning Slot
A thin rod of mass 0.9 kg and length 1 m is suspended, at rest, from one end so that it can freely oscillate in the vert...
JEE Main 2020 (Online) 5th September Evening Slot
A particle of mass 200 MeV/c2 collides with a hydrogen atom at rest. Soon after the collision the particle comes to rest...
JEE Main 2020 (Online) 5th September Morning Slot
A particle of mass m is moving along the x-axis with initial velocity $$u\widehat i$$. It collides elastically with a pa...
JEE Main 2020 (Online) 2nd September Evening Slot

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In two different experiments, an object of mass $$5 \mathrm{~kg}$$ moving with a speed of $$25 \mathrm{~ms}^{-1}$$ hits ...
JEE Main 2022 (Online) 28th July Morning Shift
A body of mass $$10 \mathrm{~kg}$$ is projected at an angle of $$45^{\circ}$$ with the horizontal. The trajectory of the...
JEE Main 2022 (Online) 27th July Evening Shift
A body of mass $$8 \mathrm{~kg}$$ and another of mass $$2 \mathrm{~kg}$$ are moving with equal kinetic energy. The ratio...
JEE Main 2022 (Online) 26th July Evening Shift
A ball of mass $$0.15 \mathrm{~kg}$$ hits the wall with its initial speed of $$12 \mathrm{~ms}^{-1}$$ and bounces back w...
JEE Main 2022 (Online) 26th July Evening Shift
Two billiard balls of mass 0.05 kg each moving in opposite directions with 10 ms$$-$$1 collide and rebound with the same...
JEE Main 2022 (Online) 25th July Evening Shift
Two bodies A and B of masses 5 kg and 8 kg are moving such that the momentum of body B is twice that of the body A. The ...
JEE Main 2022 (Online) 30th June Morning Shift
If force $$\overrightarrow F = 3\widehat i + 4\widehat j - 2\widehat k$$ acts on a particle position vector $$2\widehat... JEE Main 2022 (Online) 25th June Morning Shift An object is thrown vertically upwards. At its maximum height, which of the following quantity becomes zero? JEE Main 2022 (Online) 26th June Morning Shift Two blocks of masses 10 kg and 30 kg are placed on the same straight line with coordinates (0, 0) cm and (x, 0) cm respe... JEE Main 2022 (Online) 27th June Morning Shift A block of metal weighing 2 kg is resting on a frictionless plane (as shown in figure). It is struck by a jet releasing ... JEE Main 2022 (Online) 29th June Morning Shift Angular momentum of a single particle moving with constant speed along circular path : JEE Main 2021 (Online) 31st August Morning Shift A body of mass M moving at speed V0 collides elastically with a mass 'm' at rest. After the collision, the two masses mo... JEE Main 2021 (Online) 31st August Morning Shift Moment of inertia of a square plate of side l about the axis passing through one of the corner and perpendicular to the ... JEE Main 2021 (Online) 27th August Morning Shift A particle of mass m is suspended from a ceiling through a string of length L. The particle moves in a horizontal circle... JEE Main 2021 (Online) 26th August Evening Shift The figure shows two solid discs with radius R and r respectively. If mass per unit area is same for both, what is the r... JEE Main 2021 (Online) 27th July Morning Shift List-I List-II (a) MI of the rod (length L, Mass M, about an axis$$ \bot $$to the rod passing... JEE Main 2021 (Online) 27th July Morning Shift Two billiard balls of equal mass 30g strike a rigid wall with same speed of 108 kmph (as shown) but at different angles.... JEE Main 2021 (Online) 25th July Morning Shift A bullet of '4 g' mass is fired from a gun of mass 4 kg. If the bullet moves with the muzzle speed of 50 ms$$-$$1, the i... JEE Main 2021 (Online) 22th July Evening Shift If the Kinetic energy of a moving body becomes four times its initial Kinetic energy, then the percentage change in its ... JEE Main 2021 (Online) 20th July Evening Shift An object of mass m1 collides with another object of mass m2, which is at rest. After the collision the objects move wit... JEE Main 2021 (Online) 18th March Evening Shift Two identical blocks A and B each of mass m resting on the smooth horizontal floor are connected by a light spring of na... JEE Main 2021 (Online) 17th March Evening Shift A triangular plate is shown. A force$$\overrightarrow F $$= 4$$\widehat i-$$3$$\widehat j$$is applied at point ... JEE Main 2021 (Online) 17th March Morning Shift A large block of wood of mass M = 5.99 kg is hanging from two long massless cords. A bullet of mass m = 10 g is fired in... JEE Main 2021 (Online) 16th March Evening Shift Four equal masses, m each are placed at the comers of a square of length (l) as shown in the figure. The moment of inert... JEE Main 2021 (Online) 16th March Morning Shift Given below are two statements : one is labelled as Assertion A and the other is labelled as Reason R.Assertion A : Body... JEE Main 2021 (Online) 26th February Morning Shift Particle A of mass m1 moving with velocity$$\left( {\sqrt3\widehat i + \widehat j} \right)m{s^{ - 1}}$$collides with ... JEE Main 2020 (Online) 6th September Evening Slot A block of mass m = 1 kg slides with velocity v = 6 m/s on a frictionless horizontal surface and collides with a uniform... JEE Main 2020 (Online) 3rd September Morning Slot A particle of mass m is projected with a speed u from the ground at an angle$$\theta = {\pi \over 3}$$w.r.t. horizon... JEE Main 2020 (Online) 9th January Evening Slot Two particles of equal mass m have respective initial velocities$$u\widehat i$$and$$u\left( {{{\widehat i + \widehat ...
JEE Main 2020 (Online) 9th January Morning Slot
Three particles of masses 50 g, 100 g and 150 g are placed at the vertices of an equilateral triangle of side 1 m (as sh...
JEE Main 2019 (Online) 12th April Evening Slot
A man (mass = 50 kg) and his son (mass = 20 kg) are standing on a frictionless surface facing each other. The man pushes...
JEE Main 2019 (Online) 12th April Morning Slot
The time dependence of the position of a particle of mass m = 2 is given by $$\overrightarrow r \left( t \right) = 2t\wi... JEE Main 2019 (Online) 10th April Evening Slot A solid sphere of mass M and radius R is divided into two unequal parts. The first part has a mass of$${{7M} \over 8}$$... JEE Main 2019 (Online) 10th April Evening Slot Two particles, of masses M and 2M, moving, as shown, with speeds of 10 m/s and 5 m/s, collide elastically at the origin.... JEE Main 2019 (Online) 10th April Morning Slot A particle of mass m is moving along a trajectory given by x = x0 + a cos$$\omega $$1t y = y0 + b sin$$\omega $$2t The t... JEE Main 2019 (Online) 10th April Morning Slot A thin disc of mass M and radius R has mass per unit area$$\sigma $$(r) = kr2 where r is the distance from its centre. ... JEE Main 2019 (Online) 10th April Morning Slot A particle of mass 'm' is moving with speed '2v' and collides with a mass '2m' moving with speed 'v' in the same directi... JEE Main 2019 (Online) 9th April Evening Slot A ball is thrown vertically up (taken as +z-axis) from the ground. The correct momentum-height (p-h) diagram is : JEE Main 2019 (Online) 9th April Morning Slot A body of mass 2 kg makes an eleastic collision with a second body at rest and continues to move in the original directi... JEE Main 2019 (Online) 9th April Morning Slot A body of mass m1 moving with an unknown velocity of$${v_1}\mathop i\limits^ \wedge $$, undergoes a collinear collisio... JEE Main 2019 (Online) 8th April Evening Slot A uniform rectangular thin sheet ABCD of mass M has length a and breadth b, as shown in the figure. If the shaded portio... JEE Main 2019 (Online) 8th April Evening Slot If 1022 gas molecules each of mass 10–26 kg collide with a surface (perpendicular to it) elastically per second over an ... JEE Main 2019 (Online) 8th April Morning Slot A simple pendulum, made of a string of length$$\ell $$and a bob of mass m, is released from a small angle$${{\theta _...
JEE Main 2019 (Online) 12th January Morning Slot
The position vector of the centre of mass $$\overrightarrow r {\,_{cm}}\,$$ of an asymmetric uniform bar of negligible a...
JEE Main 2019 (Online) 12th January Morning Slot
A particle of mass m is moving in a straight line with momentum p. Starting at time t = 0, a force F = kt acts in the sa...
JEE Main 2019 (Online) 11th January Evening Slot
A rigid massless rod of length 3l has two masses attached at each end as shown in the figure. The rod is pivoted at poin...
JEE Main 2019 (Online) 10th January Evening Slot
Two masses m and $${m \over 2}$$ are connected at the two ends of a massless rigid rod of length l. The rod is suspended...
JEE Main 2019 (Online) 9th January Morning Slot
A force of $$40$$ $$N$$ acts on a point $$B$$ at the end of an $$L$$-shaped object, as shown in the figure. The angle $$... JEE Main 2018 (Online) 15th April Morning Slot A particle of mass$$m$$moving in the$$x$$direction with speed$$2v$$is hit by another particle of mass$$2m$$movi... JEE Main 2015 (Offline) This question has statement$${\rm I}$$and statement$${\rm I}{\rm I}$$. Of the four choices given after the statem... JEE Main 2013 (Offline) The figure shows the position$$-$$time$$(x-t)$$graph of one-dimensional motion of body of mass$$0.4kg.$$The mag... AIEEE 2010 Statement - 1 : Two particles moving in the same direction do not lose all their energy in a completely inelastic colli... AIEEE 2010 A bomb of mass$$16kg$$at rest explodes into two pieces of masses$$4kg$$and$$12kg.$$The velocity of the ... AIEEE 2006 A mass$$'m'$$moves with a velocity$$'v'$$and collides inelastically with another identical mass. After collision the... AIEEE 2005 A machine gun fires a bullet of mass$$40g$$with a velocity$$1200m{s^{ - 1}}. The man holding it can exert a m...
AIEEE 2004

## MCQ (More than One Correct Answer)

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A particle of mass m is moving along the side of a square of side ‘a’, with a uniform speed v in the x-y plane as shown ...
JEE Main 2016 (Offline)

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