Question

An object at rest in space suddenly explodes into three parts of same mass. The momentum of the two parts are $2 p$ i and $p \mathbf{j}$. The momentum of the third part (a) will have a magnitude $p \sqrt{3}$ (b) will have a magnitude $p \sqrt{5}$ (c) will have a magmitude $p$ (d) will have a magnitude $2 p$

Name: Problem 22, Chapter 6: Master Resource Book in JEE Main Physics
Uploaded: 2022-01-29T12:08:25-08:00
Duration: 3 min 6 s
Channel: Mirza Aslam Beig
Description: An object at rest in space suddenly explodes into three parts of same mass. The momentum of the two parts are 2 p i and p 𝐣. The momentum of the third part (a) will have a magnitude p √(3) (b) will have a magnitude p √(5) (c) will have a magmitude p (d) will have a magnitude 2 p

   An object at rest in space suddenly explodes into three parts of same mass. The momentum of the two parts are $2 p$ i and $p \mathbf{j}$. The momentum of the third part
(a) will have a magnitude $p \sqrt{3}$
(b) will have a magnitude $p \sqrt{5}$
(c) will have a magmitude $p$
(d) will have a magnitude $2 p$

Master Resource Book in JEE Main Physics

D. B. Singh 1st Edition

Chapter 6, Problem 22

Instant Answer

Solved by Expert Mirza Aslam Beig

01/29/2022

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The initial momentum of the object at rest is 0. Show more…

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An object at rest in space suddenly explodes into three parts of same mass. The momentum of the two parts are $2 p$ i and $p \mathbf{j}$. The momentum of the third part (a) will have a magnitude $p \sqrt{3}$ (b) will have a magnitude $p \sqrt{5}$ (c) will have a magmitude $p$ (d) will have a magnitude $2 p$

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Key Concepts

Calculation of Vector Magnitude

When the components of a vector are known, its magnitude can be determined using the Pythagorean theorem. This is essential in problems where the resultant momentum vector is derived from its individual components, allowing for the calculation of its overall magnitude.

Conservation of Momentum

In an isolated system with no net external forces, the total momentum is conserved. This principle means that the vector sum of the momenta of all fragments after an explosion equals the initial momentum before the explosion, which is zero if the object was initially at rest.

Vector Addition

Momentum is a vector quantity, so its components must be added using vector addition. This involves summing the momentum components in each direction independently to ensure that the net momentum in each coordinate direction is conserved.

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