An object initially at rest explodes into 3 fragments A , B and C . The momentum of A is p i ^ and that of B is 3 p j ^ , where p is a + ve number. The momentum of C will be,

2 p in a direction making angle 150 ° with that of B .

1 + 3 p in a direction making angle 120 ° with that of A .

1 + 3 p in a direction making angle 150 ° with that of B .

2 p in a direction making angle 150 ° with that of A .

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Three point like equal masses $m_{1}, m_{2}$ and $m_{3}$ are connected to the cnds of a massless rod of length $L$ which lies at rest on a smooth horizontal plane (see figure). At $t = 0,$ an explosion occurs between $m_{2}$ and $m_{3},$ and as a result, mass $m_{3}$ is detached from the rod, and moves with a known velocity $y$ at an angle of $30 °$ with the $y$ -axis. Assume that the masses $m_{2}$ and $m_{3}$ are unchanged during the explosion. What is the velocity of the centre of mass of the system consisting of three masses, after the explosion?

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Important Questions on System of Particles and Centre of Mass

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JEE Advanced

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Physics For Joint Entrance Examination JEE (Advanced): Mechanics II>Chapter 1 - System of Particles and Centre of Mass>Exercises>Q 15

Three particles of masses $1 kg, 2 kg$ and $3 kg$ are situated at the corners of an equilateral triangle move at speed $6 {ms}^{- 1},$ $3 {ms}^{- 1}$ and $2 {ms}^{- 1}$ respectively. Each particle maintains a direction towards the particle at the next corner symmetrically. Find velocity of $CM$ of the system at this instant.

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JEE Advanced

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Physics For Joint Entrance Examination JEE (Advanced): Mechanics II>Chapter 1 - System of Particles and Centre of Mass>Exercises>Q 16

An object initially at rest explodes into

3

fragments

A, B

and

C

. The momentum of

A

p \hat{i}

and that of

B

\sqrt{3 p} \hat{j}

, where

p

is a

+ ve

number. The momentum of

C

will be,

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JEE Advanced

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Physics For Joint Entrance Examination JEE (Advanced): Mechanics II>Chapter 1 - System of Particles and Centre of Mass>Exercises>Q 17

A vessel at rest explodes breaking it into three pieces. Two pieces having equal mass fly off perpendicular to one another with the same speed of

30 m / s .

The third piece has three times the mass of each of the other two pieces. What is the direction (w.r.t. the pieces having equal masses) and magnitude of its velocity immediately after the explosion?

MEDIUM

JEE Advanced

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Physics For Joint Entrance Examination JEE (Advanced): Mechanics II>Chapter 1 - System of Particles and Centre of Mass>Exercises>Q 18

A stationary body explodes into four identical fragments such that three of them fly off mutually perpendicular to each other, each with the same

KE, E_{0} .

The minimum energy of explosion will be,

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JEE Advanced

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Physics For Joint Entrance Examination JEE (Advanced): Mechanics II>Chapter 1 - System of Particles and Centre of Mass>Exercises>Q 19

A stationary body explodes into two fragments of masses

m_{1}

and

m_{2}

. If momentum of one fragment is

p

, the minimum energy of explosion is

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JEE Advanced

IMPORTANT

Physics For Joint Entrance Examination JEE (Advanced): Mechanics II>Chapter 1 - System of Particles and Centre of Mass>Exercises>Q 20

A gun of mass

M,

fires a shell of mass

m

horizontally and the energy of explosion is such as would be sufficient to project the shell vertically to a height '

h

'. The recoil velocity of the gun is

MEDIUM

JEE Advanced

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Physics For Joint Entrance Examination JEE (Advanced): Mechanics II>Chapter 1 - System of Particles and Centre of Mass>Exercises>Q 21

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

15 m s^{- 1}

each. What is the speed of the heavier fragment?

HARD

JEE Advanced

IMPORTANT

Physics For Joint Entrance Examination JEE (Advanced): Mechanics II>Chapter 1 - System of Particles and Centre of Mass>Exercises>Q 22

A particle of mass

2 m

is projected at an angle of

45 °

with horizontal with a velocity of

20 \sqrt{2} m s^{- 1}

. After

1 s

explosion takes place and the particle is broken into two equal pieces. As a result of the explosion, one part comes to rest. The maximum height attained by the other part is (Take

g = 10 m s^{- 2}

)

Important Questions on System of Particles and Centre of Mass

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