Conservation of Linear Momentum

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JEE Main 2021, 31 Aug Shift-II

A block moving horizontally on a smooth surface with a speed of $40 m/s$ splits into two parts with masses in the ratio of $1 : 2$ . If the smaller part moves at $60 m/s$ in the same direction, then the fractional change in kinetic energy is

1/3

(B)

2/3

(C)

1/8

(D)

1/4

JEE Main 2020, 9 Jan Shift-I

LEVELJEE Main

Two particles of equal mass $m$ have respective initial velocities $u \hat{i}$ and $u (\frac{i ^ + j ^}{2})$ . They collide completely inelastically. The energy lost in the process is

(A)

\frac{3}{4} m u^{2}

(B)

\frac{2}{3} m u^{2}

(C)

\frac{1}{3} m u^{2}

(D)

\frac{1}{8} m u^{2}

JEE Main 2019, 9 April Shift-II

LEVELJEE Main

A particle of mass $m$ is moving with speed $2 v$ and collides with a mass $2 m$ 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 $4 5^{\circ}$ with respect to the original direction. The speed of each of the moving particle will be

(A)

2 v

(B)

\frac{v}{2}

(C)

\frac{v}{2 2}

(D)

22 v

JEE Main 2019, 8 April Shift-II

LEVELJEE Main

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 $m_{2} = 0.5 m_{1}$ and $v_{3} = 0.5 v_{1}$ , then $v_{1}$ is

(A)

v_{4} + v_{2}

(B)

v_{4} - \frac{v _{2}}{4}

(C)

v_{4} - \frac{v _{2}}{2}

(D)

v_{4} - v_{2}

LEVELJEE Main

Statement I Two particles moving in the same direction do not lose all their energy in a completely inelastic collision. Statement II Principle of conservation of momentum holds true for all kinds of collisions.

(A)

Statement I is true, Statement II is true; Statement II is the correct explanation of Statement I

(B)

Statement I is true, Statement II is true; Statement II is not the correct explanation of Statement I

(C)

Statement I is true, Statement II is false

(D)

Statement I is false, Statement II is true

JEE Main 2021, 16 March Shift-I

LEVELJEE Main

A ball of mass $10 kg$ moving with a velocity $103 ms^{- 1}$ along X-axis, hits another ball of mass $20 kg$ , which is at rest. After collision, the first ball comes to rest and the second one disintegrates into two equal pieces. One of the pieces starts moving along Y-axis at a speed of $10 m/s$ . The second piece starts moving at a speed of $20 m/s$ at an angle $θ$ (degree) with respect to the X-axis. The configuration of pieces after collision is shown in the figure. The value of $θ$ to the nearest integer is ……… .

JEE Main 2021, 31 Aug Shift-I

LEVELJEE Main

A block moving horizontally on a smooth surface with a speed of $40 ms^{- 1}$ splits into two equal parts. If one of the parts moves at $60 ms^{- 1}$ in the same direction, then the fractional change in the kinetic energy will be $x : 4$ , where $x$ is

LEVELJEE Main

Consider the following two statements. I. Linear momentum of a system of particles is zero. II. Kinetic energy of a system of particles is zero. Then,

(A)

I does not imply II and II does not imply I

(B)

I implies II but II does not imply I

(C)

I does not imply II but II implies I

(D)

I implies II and II implies I

LEVELJEE Main

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

(A)

144 J

(B)

288 J

(C)

192 J

(D)

96 J

JEE Main 2021, 18 March Shift-I

LEVELJEE Main

A ball of mass 10 kg moving with a velocity $103$ m/s along the X-axis, hits another ball of mass 20 kg which is at rest. After the collision, first ball comes to rest while the second ball disintegrates into two equal pieces. One piece starts moving along Y-axis with a speed of 10 m/s. The second piece starts moving at an angle of 30° with respect to the X-axis. The velocity of the ball moving at 30° with X-axis is $x$ m/s. The configuration of pieces after collision is shown in the figure below. The value of $x$ to the nearest integer is .......... .

JEE Main 2020, 9 Jan Shift-II

LEVELJEE Advanced

A particle of mass $m$ is projected with a speed $u$ from the ground at an angle $θ = \frac{π}{3}$ w.r.t. horizontal (X-axis). When it has reached its maximum height, it collides completely inelastically with another particle of the same mass and velocity $u \hat{i}$ . The horizontal distance covered by the combined mass before reaching the ground is

(A)

\frac{3 3}{8} \frac{u ^{2}}{g}

(B)

\frac{3 2}{4} \frac{u ^{2}}{g}

(C)

\frac{5}{8} \frac{u ^{2}}{g}

(D)

22 \frac{u ^{2}}{g}

JEE Main 2019

LEVELJEE Advanced

A wedge of mass $M = 4 m$ 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

(A)

\frac{2 v ^{2}}{7 g}

(B)

\frac{v ^{2}}{g}

(C)

\frac{2 v ^{2}}{5 g}

(D)

\frac{v ^{2}}{2 g}

JEE Main 2019, 12 April Shift-I

LEVELJEE Main

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

(A)

0.28 ms^{- 1}

(B)

0.20 ms^{- 1}

(C)

0.47 ms^{- 1}

(D)

0.14 ms^{- 1}

JEE Main 2021, 22 July Shift-II

LEVELJEE Main

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 impulse imparted to the gun and velocity of recoil of gun are

(A)

0.4 kg-ms^{- 1}, 0.1 ms^{- 1}

(B)

0.2 kg-ms^{- 1}, 0.05 ms^{- 1}

(C)

0.2 kg-ms^{- 1}, 0.1 ms^{- 1}

(D)

0.4 kg-ms^{- 1}, 0.05 ms^{- 1}

JEE Advanced 1979

LEVELJEE Main

When a ball is thrown up, the magnitude of its momentum decreases and then increases. Does this violate the conservation of momentum principle?

JEE Advanced 1979

LEVELJEE Main

A $20 g$ bullet pierces through a plate of mass $M_{1} = 1 kg$ and then comes to rest inside a second plate of mass $M_{2} = 2.98 kg$ as shown in the figure. It is found that the two plates initially at rest, now move with equal velocities. Find the percentage loss in the initial velocity of the bullet when it is between $M_{1}$ and $M_{2}$ . Neglect any loss of material of the plates due to the action of bullet. Both plates are lying on smooth table.

JEE Advanced 1981

LEVELJEE Main

A body of mass $1$ kg initially at rest, explodes and breaks into three fragments of masses in the ratio $1 : 1 : 3$ . The two pieces of equal mass fly-off perpendicular to each other with a speed of $30$ m/s each. What is the velocity of the heavier fragment ?

JEE Advanced 1998

LEVELJEE Advanced

A cylindrical solid of mass $1 0^{- 2} kg$ and cross-sectional area $1 0^{- 4} m^{2}$ is moving parallel to its axis (the x-axis) with a uniform speed of $1 0^{3} m/s$ in the positive direction. At $t = 0$ , its front face passes the plane $x = 0$ . The region to the right of this plane is filled with stationary dust particles of uniform density $1 0^{- 3} kg/m^{3}$ . When a dust particle collides with the face of the cylinder, it sticks to its surface. Assuming that the dimensions of the cylinder remain practically unchanged and that the dust sticks only to the front face of the cylinder find the x-coordinate of the front of the cylinder at $t = 150 s$ .

JEE Advanced 2011

LEVELJEE Advanced

A ball of mass $0.2 kg$ rests on a vertical post of height $5 m$ . A bullet of mass $0.01 kg$ , travelling with a velocity $v m/s$ in a horizontal direction, hits the centre of the ball. After the collision, the ball and bullet travel independently. The ball hits the ground at a distance of $20 m$ and the bullet at a distance of $100 m$ from the foot of the post. The initial velocity $v$ of the bullet is

(A)

250 m/s

(B)

2502 m/s

(C)

400 m/s

(D)

500 m/s

JEE Advanced (1997)

LEVELJEE Advanced

A cart is moving along $x$ -direction with a velocity of $4 m/s$ . A person on the cart throws a stone with a velocity of $6 m/s$ relative to himself. In the frame of reference of the cart, the stone is thrown in $y$ - $z$ plane making an angle of $3 0^{\circ}$ with vertical $z$ -axis. At the highest point of its trajectory, the stone hits an object of equal mass hung vertically from branch of a tree by means of a string of length $L$ . A completely inelastic collision occurs, in which the stone gets embedded in the object. Determine ( $g = 9.8 m/s^{2}$ ) (a) the speed of the combined mass immediately after the collision with respect to an observer on the ground. (b) the length $L$ of the string such that tension in the string becomes zero when the string becomes horizontal during the subsequent motion of the combined mass.

JEE Advanced 1987

LEVELJEE Main

A particle of mass $4 m$ which is at rest explodes into three fragments. Two of the fragments each of mass $m$ are found to move with a speed $v$ each in mutually perpendicular directions. The total energy released in the process of explosion is ......... .

JEE Advanced (2001)

LEVELJEE Main

Two particles of masses $m_{1}$ and $m_{2}$ in projectile motion have velocities $v_{1}$ and $v_{2}$ respectively at time $t = 0$ . They collide at time $t_{0}$ . Their velocities become $v_{1}^{'}$ and $v_{2}^{'}$ at time $2 t_{0}$ while still moving in air. The value of $∣ (m_{1} v_{1}^{'} + m_{2} v_{2}^{'}) - (m_{1} v_{1} + m_{2} v_{2}) ∣$ is

(A)

zero

(B)

(m_{1} + m_{2}) g t_{0}

(C)

2 (m_{1} + m_{2}) g t_{0}

(D)

\frac{1}{2} (m_{1} + m_{2}) g t_{0}

JEE Advanced 2009

LEVELBoard

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

(A)

linear momentum of the system does not change in time

(B)

kinetic energy of the system does not change in time

(C)

angular momentum of the system does not change in time

(D)

potential energy of the system does not change in time

JEE Advanced (1982)

LEVELJEE Main

Three particles $A, B$ and $C$ of equal mass move with equal speed $v$ along the medians of an equilateral triangle as shown in figure. They collide at the centroid $G$ of the triangle. After the collision, $A$ comes to rest, $B$ retraces its path with the speed $v$ . What is the velocity of $C$ ?

JEE Advanced (1986)

LEVELJEE Main

A shell is fired from a cannon with a velocity $v$ (m/s) at an angle $θ$ with the horizontal direction. At the highest point in its path it explodes into two pieces of equal mass. One of the pieces retraces its path to the cannon and the speed (m/s) of the other piece immediately after the explosion is

(A)

3 v cos θ

(B)

2 v cos θ

(C)

\frac{3}{2} v cos θ

(D)

\frac{3}{2} v cos θ

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } Two particles of equal mass m have respective initial velocities ui^ and u(2i^+j^​​). They collide completely inelastically. The energy lost in the process is

Statement I Two particles moving in the same direction do not lose all their energy in a completely inelastic collision. Statement II Principle of conservation of momentum holds true for all kinds of collisions.

Consider the following two statements. I. Linear momentum of a system of particles is zero. II. Kinetic energy of a system of particles is zero. Then,

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } A bomb of mass 16 kg at rest explodes into two pieces of masses 4 kg and 12 kg. The velocity of the 12 kg mass is 4 ms−1. The kinetic energy of the other mass is

When a ball is thrown up, the magnitude of its momentum decreases and then increases. Does this violate the conservation of momentum principle?

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 particles of equal mass $m$ have respective initial velocities $u \hat{i}$ and $u (\frac{i ^ + j ^}{2})$ . They collide completely inelastically. The energy lost in the process is

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