Question

The masses of two bodies in the ratio of 4:5and their velocities are 1:3 then their linear momentum will be the ratio of _​

Answer 1

Given Information :

• Ratio of the masses of two bodies = 4:5
• Ratio of their velocities = 1:3

To calculate :

• Ratio of their linear momentum.

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Before commencing the steps, let's take a took a look at the description of momentum.

Momentum is defined as the product of mass and velocity.

$\longrightarrow\sf{Momentum = Mass \times Velocity}$

$\longrightarrow\sf{\vec{P} = m \times \vec{V}}$

• It is a vector quantity.
• Direction of momentum is in the direction of the velocity.
• SI unit of momentum is kg.m/s.

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Now, coming back to the question,

Let us suppose the masses of those two bodies as 4x kg and 5x kg respectively. And, let us suppose the velocities of those two bodies as y m/s and 3y m/s.

• Mass of $\sf m_1$ = 4x kg
• Mass of $\sf m_2$ = 5x kg
• Velocity of $\sf v_1$ = y m/s
• Velocity of $\sf v_2$ = 3y m/s

Now, ratio of the linear momentum of these two bodies will be given by,

$\quad \twoheadrightarrow\sf { Ratio = \dfrac{P′}{P′′} }$

$\quad \twoheadrightarrow\sf { Ratio = \dfrac{m_1v_1}{m_2v_2} }$

$\quad \twoheadrightarrow\sf { Ratio = \cancel{\dfrac{4xy \; kg.ms^{-1}}{15xy \; kg.ms^{-1}}} }$

$\quad \twoheadrightarrow\underline{\boxed{\textbf{\textsf { Ratio = 4:15 }}}}$

Therefore, their linear momentum will be the ratio of 4:15.

Answer 2

Question:-

• The masses of two bodies in the ratio of 4:5and their velocities are 1:3 then their linear momentum will be the ratio of

Given information:-

• Ratio of the masses of the two bodies=4:5
• Ratio of their velocities =1:3

To find:-

• We have to calculate Ratio of their linear momentum.

Formula used:-

We know that Momentum is defined as the product of maas and velocity.

$\large\underline{\sf{Momentum=Mass×Velocity}}$

$\large\underline{\sf{P=m×V}}$

______________________________________

Let's look at a description of Momentum.

• It is a vector quantity.
• Direction of momentum is in the direction of the velocity.
• SI unit of momentum is kg.m/s

______________________________________

Now,coming back to the question:-

Let us suppose the masses of those two bodies as 4x and 5x kg respectively.

Let us suppose the velocity of two bodies as y m/s and 3y m/s.

$\large\underline{\sf{Mass \: of \: m_{1} = 4x \: kg}}$

$\large\underline{\sf{Mass \: of \: m_{2}=5x \: kg}}$

$\large\underline{\sf{Velocity \: of \: v_{1} = y \: \: m/s }}$

$\large\underline{\sf{Velocity \: of v_{2} = 3y \: \: m/s}}$

Ratio of linear momentum:-

$\large{\sf{ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: Ratio = \frac{P'}{P''} }}$

$\large{\sf{ \: \: \: \: \: \: \: \: \: \: \: \: \: \: Ratio = \frac{m_{1} v_{1} }{m_{2} v_{2}} }}$

$\large{\sf{ \: \: \: \: \: Ratio = \frac{4xy \: \: kg. {ms}^{ - 1} }{15xy \: \: kg. {ms}^{ - 1} } }}$

$\huge\boxed {\boxed{ \boxed{\sf{ \red{Ratio = 4 \ratio 15}}}}}$