Conservation of Momentum — JEE Main PYQs

Four particles A, B, C and D with masses $m_A=m,m_B=2m,m_c=3m$ and $m_D=4m$ are at the corners of a square. They have accelerations of equal magnitude with directions as shown. The acceleration of the centre of mass of the particles is:

A body of mass $m_1$ moving with an unknown velocity of $v_1\hat{i}$ undergoes a collinear collision with a body of mass $m_2$ moving with a velocity $v_2\hat{i}$. After collision $m_1$ and $m_2$ move with velocities of $v_3\hat{i}$ and $v_4\hat{i}$ respectively. If $m_2=0.5m_1$ …

A uniform rectangular thin sheet $ABCD$ of mass $M$ has length $a$ and breadth $b$, as shown in the figure. If the shaded portion HBGO is cut off, the coordinates of the centre of mass of the remaining portion will be:

A body of mass 2 kg makes an elastic collision with a second body at rest and continues to move in the original direction but with one fourth of its original speed. What is the mass of the second body?

A piece of wood of mass 0.03 kg is dropped from the top of a 100 m height building. At the same time, a bullet of mass 0.02 kg is fired vertically upward, with a velocity $100{\mathrm{ms}}^{-}{}^1$, from the ground. The bullet gets embedded in the wood. Then the maximum heigh …

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 same direction on the moving particle during time interval $T$ so that its momentum changes from $p$ to $3p$. Here $k$ is a constant. The value of $T$ is:

A man (mass $=50\mathrm{kg}$) and his son (mass $=20\mathrm{kg}$) are standing on a frictionless surface facing each other. The man pushes his son so that he starts moving at a speed of 0.70 ${\mathrm{ms}}^{-1}$ with respect to the man. The speed of the man with respect to the …

A liquid of density $\rho$ is coming out of a hose pipe of radius a with horizontal speed $v$ and hits a mesh. 50% of the liquid passes through the mesh unaffected. 25% looses all of its momentum and $25\%$ comes back with the same speed. The resultant pressure on the mes …

The position vector of the centre of mass $\overrightarrow{\mathrm{r}}\mathrm{cm}$ of an asymmetric uniform bar of negligible area of cross-section as shown in figure is:

A simple pendulum, made of a string of length I and a bob of mass m , is released from a small angle ${\theta }_0$. It strikes a block of mass M , kept on a horizontal surface at its lowest point of oscillations, elastically. It bounces back and goes up to an angle …

Three particles of masses $50\mathrm{g}$, $100\mathrm{g}$ and $150$ g are placed at the vertices of an equilateral triangle of side 1 m (as shown in the figure). The $(x,y)$ coordinates of the centre of mass will be :

An alpha-particle of mass $m$ suffers 1-deminsional elastic collision with a nucleus at rest of unknown mass. It is scattered directly backwards losing, 64% of its initial kinetic energy. The mass of the nucleus is :

A particle P is formed due to a completely inelastic collision of particles x and y having de - Broglie wavelengths ${\lambda }_{\mathrm{x}}$ and ${\lambda }_{\mathrm{y}}$ respectively. If x and y were moving in opposite directions, then the de - Broglie wavelength of $P$ is:

A particle of mass $m$ is moving with speed $2v$ collides with a mass $2m$ moving with speed v in the same direction. After collision, the first mass is stopped completely while the second one splits into two particles each of mass m, which move at angle $45^0$ with respect to …

A wedge of mass $M=4m$ lies on a frictionless plane. A particle of mass $m$ approaches the wedge with speed v. There is no friction between the particle and the plane or between the particle and the wedge. The maximum height climbed by the particle on the wedge is given by:

Three blocks $\mathrm{A},\mathrm{B}$ and C are lying on a smooth horizontal surface, as shown in the figure. $A$ and $B$ have equal masses, $m$ while $C$ has mass $M$. Block $A$ is given an initial speed $v$ towards B due to which it collides with B perfectly ine …

Two particles, of masses M and 2M, moving as shown, with speeds of $10\mathrm{m}/\mathrm{s}$ and $5\mathrm{m}/\mathrm{s}$, collide elastically at the origin. After the collision, they move along the indicated directions with speeds $v_1$ and $v_2$ respectively. The value …

In a collinear collision, a particle with an initial speed $v_0$ strikes a stationary particle of the same mass. If the final total kinetic energy is $50\%$ greater than the original kinetic energy, the magnitude of the relative velocity between the two particles, after co …

It is found that if a neutron suffers an elastic collinear collision with deuterium at rest, fractional loss of its energy is $p_d$; while for its similar collision with carbon nucleus at rest, fractional loss of energy is $p_c$. The values of $p_d$ and $p_c$ are respectively:

The mass of a hydrogen molecule is $3.32\times 10^{-27}$ kg. If $10^{23}$ hydrogen molecules strike, per second, a fixed wall of area $2$ cm${}^2$ at an angle of $45^{\circ }$ to the normal, and rebound elastically with a speed of $10^3$ m/s, then the pressure on the wall is nearly …

Distance of the centre of mass of a solid uniform cone from its vertex is ${\mathrm{z}}_0$. If the radius of its base is R and its height is h then ${\mathrm{z}}_0$ is equal to :

A particle of mass $m$ moving in the $x$ direction with speed $2v$ is hit by another particle of mass $2m$ moving in the y direction with speed v. If the collision is perfectly inelastic, the percentage loss in the energy during the collision is close to

This question has Statement I and Statement II. Of the four choices given after the Statements, choose the one that best describes the two Statements.
Statement I : A point particle of mass m moving with speed v collides with stationary point particle of mass M . If the maximum e …

Statement-1: Two particles moving in the same direction do not lose all their energy in a completely inelastic collision.

Statement-2: Principle of conservation of momentum holds true for all kinds of collisions.

The figure shows the position - time $(x-t)$ graph of one-dimensional motion of a body of mass 0.4 kg . The magnitude of each impulse is

A thin rod of length 'L' is lying along the $x$-axis with its ends at $x=0$ and $x=L$. Its linear density (mass/length) varies with $x$ as $k{\left(\frac{x}{L}\right)}^n$, where $n$ can be zero or any positive number. If the position $x_{CM}$ of the centre of mass o …

A block of mass 0.50 kg is moving with a speed of $2.00\mathrm{m}/\mathrm{s}$ on a smooth surface. It strikes another mass of 1.00 kg and then they move together as a single body. The energy loss during the collision is

A circular disc of radius $R$ is removed from a bigger circular disc of radius $2R$ such that the circumferences of the discs coincide. The centre of mass of the new disc is $\alpha R$ from the centre of the bigger disc. The value of $\alpha$ is

A bomb of mass 16 kg at rest explodes into two pieces of masses of 4 kg and 12 kg. The velocity of the 12 kg mass is $4{\text{ms}}^{-1}$. The kinetic energy of the other mass is

A player caught a cricket ball of mass 150 g moving at a rate of $20\text{m/s}$. If the catching process is completed in 0.1 s, the force of the blow exerted by the ball on the hand of the player is equal to

Consider a two particle system with particles having masses $m_1$ and $m_2$. If the first particle is pushed towards the centre of mass through a distance d, by what distance should the second particle be moved, so as to keep the centre of mass at the same position?

A body A of mass M while falling vertically downwards under gravity breaks into two parts; a body B of mass $1/3\mathrm{M}$ and a body C of mass $2/3\mathrm{M}$. The centre of mass of bodies B and C taken together shifts compared to that of body A towards

A mass '$m$' moves with a velocity $v$ and collides inelastically with another identical mass. After collision the $1^{\text{st }}$ mass moves with velocity $\mathrm{v}/\sqrt{}3$ in a direction perpendicular to the initial direction of motion. Find the speed of the …

A machine gun fires a bullet of mass 40 g with a velocity $1200{\mathrm{ms}}^{-1}$. The man holding it can exert a maximum force of 144 N on the gun. How many bullets can he fire per second at the most?