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Three spheres of different materials are in motion their radii, densities and speeds are as given
Sl. no Radius Density Speed
1
2
3
r
r/2
2r
d
d
d/2
v
v/2
v
If K₁,K₂,K₃ are the kinetic energies of those three spheres respectively, those values can be arranged in descending order as given below

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K₂,K₁,K₃

K₃,K₂,K₁

K₁,K₂,K₃

K₃,K₁,K₂

answer is B.

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Detailed Solution

From the question,

$K_{1} = \frac{1}{2} {mv}^{2}$

substituting the values,

$= \frac{1}{2} \times d \times \frac{4}{3} {πr}^{3} \times v^{2}$

where r is the sphere's radius and d is its density.

Similarly,

$k_{2} = \frac{1}{2} \times d \times \frac{4}{3} \times π \times {(\frac{r}{2})}^{3} \times {(\frac{v}{2})}^{2}$

$K_{3} = \frac{1}{2} \times \frac{d}{2} \times \frac{4}{3} \times π \times {(2 r)}^{3} \times v^{2}$

thus we can conclude that $K_{3} > K_{1} > K_{2} .$

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