Conservation of Momentum — JEE Advanced PYQs

A uniform circular disk of radius 0.2 m and mass 1 kg is pivoted at its top point $C$ such that it can rotate freely around $C$ in the $XY$ plane, as shown in the figure. Initially, when the disk is at rest, a particle of mass 20 g, travelling along negative $x$ direction …

In a scattering experiment, a particle of mass $2m$ collides with another particle of mass $m$, which is initially at rest. Assuming the collision to be perfectly elastic, the maximum angular deviation $\theta$ of the heavier particle, as shown in the figure, in radians is …

Two particles, 1 and 2, each of mass $m$, are connected by a massless spring, and are on a horizontal frictionless plane, as shown in the figure. Initially, the two particles, with their center of mass at $x_0$, are oscillating with amplitude $a$ and angular frequency $\omega$. …

Two particles, 1 and 2, each of mass $m$, are connected by a massless spring, and are on a horizontal frictionless plane, as shown in the figure. Initially, the two particles, with their center of mass at $x_0$, are oscillating with amplitude $a$ and angular frequency $\omega$. …

A heavy nucleus $N$, at rest, undergoes fission $N\to P+Q$, where $P$ and $Q$ are two lighter nuclei. Let $\delta =M_N-M_P-M_Q$, where $M_P,M_Q$ and $M_N$ are the masses of $P,Q$ and $N$, respectively. $E_P$ and $E_Q$ are the kineti …

A projectile is thrown from a point O on the ground at an angle 45° from the vertical and with a speed $5\sqrt{2}$ m/s. The projectile at the highest point of its trajectory splits into two equal parts. One part falls vertically down to the ground, 0.5 s after the splitting. The …

A projectile is thrown from a point O on the ground at an angle 45° from the vertical and with a speed $5\sqrt{2}$ m/s. The projectile at the highest point of its trajectory splits into two equal parts. One part falls vertically down to the ground, 0.5 s after the splitting. The …

A spring-block system is resting on a frictionless floor as shown in the figure. The spring constant is $2.0\mathrm{N}{\mathrm{m}}^{-1}$ and the mass of the block is 2.0 kg. Ignore the mass of the spring. Initially the spring is in an unstretched condition. Another block of mas …

A block of mass $M$ has a circular cut with a frictionless surface as shown. The block rests on the horizontal frictionless surface of a fixed table. Initially the right edge of the block is at $x=0$, in a co-ordinate system fixed to the table. A point mass $m$ is released …

A horizontal circular platform of radius $0.5m$ and mass $0.45kg$ is free to rotate about its axis. Two massless spring toy-guns, each carrying a steel ball of mass 0.05 kg are attached to the platform at a distance $0.25m$ from the centre on its either sides along its …

A particle of mass $m$ is projected from the ground with an initial speed $u_0$ at an angle $\alpha$ with the horizontal. At the highest point of its trajectory, it makes a completely inelastic collision with another identical particle, which was thrown vertically upward …

A ball of mass 0.2 kg rests on a vertical post of height 5 m . A bullet of mass 0.01 kg, traveling with a velocity $\mathrm{Vm}/\mathrm{s}$ in a horizontal direction, hits the centre of the ball. After the collision, the ball and bullet travel independently. The bal …

A point mass of 1 kg collides elastically with a stationary point mass of 5 kg. After their collision, the 1 kg mass reverses its direction and moves with a speed of $2{\mathrm{ms}}^{-1}$. Which of the following statement(s) is (are) correct for the system of these two masses ?

Three objects A, B and C are kept in a straight line on a frictionless horizontal surface. These have masses $m,2m$ and $m$, respectively. The object A moves towards B with a speed 9 m/s and makes an elastic collision with it. Thereafter, B makes completely inelastic collis …

Look at the drawing given in the figure which has been drawn with ink of uniform line-thickness. The mass of ink used to draw each of the two inner circles, and each of the two line segments is $m$. The mass of the ink used to draw the outer circle is $6m$. The coordinates o …

Two small particles of equal masses start moving in opposite directions from a point A in a horizontal circular orbit. Their tangential velocities are $v$ and $2v$, respectively, as shown in the figure. Between collisions, the particles move with constant speeds. After makin …

If the resultant of all the external forces acting on a system of particles is zero, then from an inertial frame, one can surely say that

Two balls, having linear momenta ${\vec{p}}_1=p\hat{i}$ and ${\vec{p}}_2=-p\hat{i}$, undergo a collision in free space. There is no external force acting on the balls. Let ${\vec{p}}_1^{\prime }$ and ${\vec{p}}_2^{\prime }$ be their final momenta. The following option(s) …

STATEMENT-1
In an elastic collision between two bodies, the relative speed of the bodies after collision is equal to the relative speed before the collision.
because
STATEMENT-2
In an elastic collision, the linear momentum of the system is conserved.

STATEMENT-1
If there is no external torque on a body about its center of mass, then the velocity of the center of mass remains constant.
because
STATEMENT-2
The linear momentum of an isolated system remains constant.