Question

Two bodies of equal masses are moving with uniform velocities v & 2v. Find the ratio
eir kinetic energies. ​

Answer 1

Answer:

Mass of bodies is equal ( let's assume it as "m")

Velocity of one object is "v" and that of another is "2v".

To find:

Ratio of Kinetic energy of the objects

Concept:

Kinetic energy is the energy possessed by the object by the virtue of its velocity.

It is different from Potential Energy which is obtained by virtue of its Position

Formulas used:

KE = ½MV² ,

where mass=> M and velocity =>V

Calculation:

KE of 1st object

KE1 = ½mv² .........(1)

KE of 2nd body

KE2 = ½m(2v)²

=> KE2 = ½m4v²

=> KE2 = 4 (½mv²) ........(2)

Now , required ratio is

KE1 : KE2 = ½mv² : 4 (½mv²) = 1:4

So final answer is

$\huge{\boxed{Ratio \: =\: 1:4}}$

Answer 2

$\Large{\underline{\underline{\red{\mathfrak{Answer :}}}}}$

Ratio =

$\large{\underline{\underline{\red{\mathfrak{Step-By-Step-Explanation :}}}}}$

$\tt Given \begin{cases} \sf{Masses \: of \: object \: are \: equal} \\ \sf{Velocities \: are \: v \: and \: 2v} \end{cases}$

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To Find :

Ratio of Kinetic Energies is 1:4

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Solution :

We have formula for Kinetic Energy :

$\Large{\underline{\boxed{\rm{K.E \: = \: \frac{1}{2} \: mv^2}}}}$

Put velocity = v for First Case,

⇒K.E1 = ½ * mv²

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Now take velocity = 2v

⇒K.E = ½ * m(2v)²

⇒K.E = ½*m4v²

We have to find Ratios

So,

$\Large \rightarrow {\rm{\frac{K.E_1}{K.E_2} \: = \: \frac{\cancel{\frac{1}{2}} \: \cancel{m} \cancel{v^2}}{\cancel{\frac{1}{2}} \: \cancel{m}4 \cancel{v^2}}}}$

So,

$\large \rightarrow {\rm{\frac{K.E_1}{K.E_2} \: = \: \frac{1}{4}}}$

$\LARGE \implies {\boxed{\boxed{\sf{K.E_1 : K.E_2 \: = \: 1:4}}}}$

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