Question

What will be the change in kinetic energy if velocity is tripled and mass is doubled? Find the ratio of kinetic energies?​

Answer 1

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Answer

ratio of kinetic energies is 18 : 1

Given

→ Velocity is tripled

→  Mass is doubled

To Find

→ Ratio of energies

Solution

Kinetic energy of a body is given by ,

$\blue{\bigstar}\ \; \bf K=\dfrac{1}{2}mv^2$

where ,

• m denotes mass of the body
• v denotes velocity of the body

⊕  If velocity is tripled and mass is doubled , then

→  v' = 3v

→  m' = 2m

Let new kinetic energy be K'

$\to \rm K'=\dfrac{1}{2}m'(v')^2\\\\\to \rm K'=\dfrac{1}{2}(2m)(3v)^2\\\\\to \bf K'=9mv^2$

Let's find the ratio b/w kinetic energies ,

$\to \rm \dfrac{K'}{K}=\dfrac{9mv^2}{\frac{1}{2}mv^2}\\\\\to \rm \dfrac{K'}{K}=\dfrac{9\times 2}{1}\\\\\to \bf \dfrac{K'}{K}=\dfrac{18}{1}\ \; \orange{\bigstar}$

So , the ratio of kinetic energies b/w new and old  is 18:1

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Answer 2

(»•«)

To Find: Ratio of the kinetic energies if the velocity is tripled and the mass doubled.

Let,

Mass of the object (m) = m′

Velocity of the object (v) = v′

We know,

Eₖ = ½mv²

where,

• Eₖ = Kinetic energy,
• m = Mass &
• v = Velocity.

∴ Kinetic energy of the object is = ½m′v′².

After the change:-

Mass becomes (m) = 2m′

Velocity (v) = 3v′

∴ Kinetic energy of the object becomes =

½(2m′)(3v′)²

= (m′)(9v′²)

= 9m′v′²

Finding ratio of Kinetic energy changed :-

i.e.,

(½m′v′²)/(9m′v′²)

= (½)(9)

= 1/18

☞ Ratio of the change of kinetic energy is (1/18).