Question

Two bodies have equal mass. However, the speed of the body is twice the speed of other body. What is the ratio of Kinetic Energy of two bodies?

Answer 1

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Answer 2

Answer:

The ratio of Kinetic energy of two bodies will be 1 : 4.

Explanation:

• Kinetic energy is the energy posses by a body due to its state of motion.
• It is defined as the work needed to be done to accelerate a body of given mass 'm' from the rest to a certain velocity 'v'.

       $K.E. =\frac{1}{2}mv^2$

⇒   K.E.  ∝ m  and   K.E. ∝ v²

Consider that first body has mass 'm₁' and velocity 'v₁' and the second body has mass 'm₂' and velocity 'v₂'.

We have given, m₁ = m₂ = m

Therefore, $K.E._{1}=\frac{1}{2}mv_{1}^2$        and     $K.E._{2}=\frac{1}{2}mv_{2}^2$

Given,  v₁ = 2v₂

⇒  $K.E._{1}=\frac{1}{2}m(2v_{2})^2$

⇒  $K.E._{1}=4*\frac{1}{2}mv_{2}^2$

⇒ $K.E._{1}=4*K.E_{2}$

∴  $\frac{K.E._{1}}{K.E. _{2}} =\frac{4}{1}$

Therefore, the ratio of kinetic energy is K.E.₁ : K.E.₂ = 4 : 1