Question

Two bodies of equal masses move with uniform velocity v and 3v respectively find the ratio of their kinetic energies

Answer 1

kinetic energy = 1/2 mv^2
kinetic energy ratio = 1:9

Answer 2

Answer :-

The ratio of the kinetic energies is 1 : 9 .

Given :-

Two bodies of equal masses move with uniform velocity v and 3v respectively

To find :-

• Ratio of their kinetic energies

Solution :-

The masses of the two bodies are equal .

So,

Let the mass of the each body be m.

( i ) Mass of first body = m.

Velocity of first body = v

So ,

K.E of first body = 1/2mv² ......( eq 1 )

( ii ) Mass of second body = m

Velocity of second body = 3v

So ,

• K.E of second body = 1/2m( 3v)²

⇢ 1/2m × 9v²

⇢ 9/2mv². .....( eq 2 )

Now, to find out the ration of kinetic energies of the two bodies ,

we should divide Equation ( 1 ) by equation ( 2 ) , so that

K.E of first body / K.E of second body= 1/2mv²÷ 9/2mv²

K.E of first body / K.E of second body = 1/9

Hence,

The ratio of the kinetic energies is 1 : 9

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❥ Extra shots :-

• The energy possessed by a body by virtue of its motion is known as kinetic energy.
•    A moving car is an example of kinetic energy.
• K.E. = 1 /2 mv²

Here, "m" is the mass of the body and "v" is the velocity.

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