Question

A body of mass 6 kg has a momentum pf 3000 kg ms-¹. what will be the momentum of body if mass and velocity are doubled.​

Answer 1

Given :

• Mass of the body = 6 kg
• Momentum of the body = 3000 kg ms-¹

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To Find :

• Momentum of the body if mass and velocity are doubled = ?

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Solution :

~ How to Solve :

Here ,we have been provided with the mass and momentum so ,by using the formula p = mv we can calculate the velocity of the body .After that ,by doubling the mass and velocity we can get the momentum if mass and velocity are doubled. Let's Solve :

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~ Formula Used :

$\large{\pink{\dashrightarrow \: \: {\underbrace{\underline{\purple{\pmb{\sf{ p = Mass \times Velocity}}}}}}}}$

Where :

• ➳ p = Momentum
• ➳ m = Mass
• ➳ v = Velocity

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~ Calculating the Velocity of body :

$:\longmapsto \qquad \sf {p = mv } \\ \\ :\longmapsto \qquad \sf {3000 = 6 \times v } \\ \\ :\longmapsto \qquad \sf {\dfrac{3000}{6} = v } \\ \\ :\longmapsto \qquad \sf {\cancel\dfrac{3000}{6} = v } \\ \\ {\qquad{\textsf{ Velocity of the body = {\color{green}{\sf{ 500 \: m/s-¹ }}}}}}$

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~ Momentum if mass and velocity are doubled :

• Doubled Mass :

$\qquad{\color{maroon}{\rightarrowtail}} \:$ Mass = 2 × 6 = ${\red{\sf{ 12 \: kg}}}$

• Doubled Velocity :

$\qquad{\color{maroon}{\rightarrowtail}} \:$ Velocity = 2 × 500 = ${\red{\sf{ 1000 \: ms-¹ }}}$

~ Let's Calculate the Momentum :

${:\implies{\qquad{\sf{ p = mv }}}} \\ \\ \ {:\implies{\qquad{\sf{ p = 12 \times 1000 }}}} \\ \\ \ {\qquad{\sf{ Momentum \: of \: the \: body{\small_{(Doubled \: Mass \: and \: Velocity)}} = {\orange{\sf{ 12000 \: kg \: ms-¹ }}}}}}$

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Therefore :

❝ If mass and velocity of the object is doubled than its momentum will be 12000 kg ms-¹ . ❞

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Answer 2

Given :-

• mass of the body = 6 kg
• Momentum = 3000 kg m/s

To find :-

• Momentum of the body if mass and velocity are doubled

Formula Used :-

• Momentum = mass x velocity

Solution :-

First of all we will find out the velocity. Therefore,

-> 3000 = 6 x v

-> 6v = 3000

-> v = 3000/6

-> v = 500

Therefore now we will double the velocity and the mass . So we get,

• New mass = 2 x 6 = 12 kg
• Velocity = 500 x 2 = 1000 m/s

Therefore the new momentum will be,

-> 12 x 1000

-> 12000 kg m/s

Therefore if the velocity and mass gets doubled then the new momentum will be 12000 kg m/s