Question

A body of mass m moving with velocity v and its
momentum is p. Another body has mass double than the first one, its velocity is also double and its Momentum p'
. What is the relation between p and p'​

Answer 1

Solution:

As per the given data,

• Mass = m
• Velocity = v

The momentum of the body is given by,

⇒ P = mv

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Now,

• Mass (m') = 2m
• Velocity(v') = 2v

The momentum of the body is given by,

⇒ P' = m' v '

⇒ P' = 2m x 2v

⇒ P' = 4mv

_________________

Now,

$\implies\sf{\dfrac{P}{P'} = \dfrac{2mv}{4mv}}$

$\implies\sf{\dfrac{P}{P'} = \dfrac{1}{2}}$

$\implies\boxed{\sf{P' = 2P}}$

Answer 2

$\huge{\textbf{\textsf{{☆ AN}}{\purple{SW}}{\pink{ER ☆} \: {{}{}}}}}$

• Mass = m
• Velocity = v

• For calculating momentum of body

$\begin{gathered}\begin{gathered}\mapsto \sf\boxed{\bold{\orange{P = mv}}}\\\end{gathered}\end{gathered}$

Mass (m') = 2m

Velocity(v') = 2v

Now,

⇒ P' = m' v '

⇒ P' = 2m x 2v

⇒ P' = 4mv

$\begin{gathered}\implies\sf{\dfrac{P}{P'} = \dfrac{2mv}{4mv}}\\ \\\end{gathered}$

$\begin{gathered}\implies\sf{\dfrac{P}{P'} = \dfrac{1}{2}}\\ \\\end{gathered}$

$\begin{gathered}\begin{gathered}\sf\boxed{\bold{\blue{P' = 2P}}}\\\end{gathered}\end{gathered}$