Question

Two lead Spheres have radii in the ratio 1:2 and have the same linear momentum.the ratio of there kinetic energy is?

Answer 1

The answer is 8:1

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Answer 2

Explanation:

Kinetic energy of an object in terms of its momentum is given by :

$K=\dfrac{p^2}{2m}$

m is mass of an object

It is given that the lead sphere are in the ratio of 1:2.

Density is given by mass per unit volume. Density is same for both. Density is directly proportional to mass. So,

$\dfrac{K_1}{K_2}=\dfrac{m_2}{m_1}=(\dfrac{r_2}{r_1})^3\\\\\dfrac{K_1}{K_2}=(\dfrac{r_2}{r_1})^3\\\\\dfrac{K_1}{K_2}=(\dfrac{2}{r_1})^3\\\\\dfrac{K_1}{K_2}=\dfrac{8}{1}$

So, the ratio of their kinetic energy is 8:1.

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Momentum

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