Question

two spheres of same materials are moving with kinetic energies in the ratio 108 : 576. if the ratio of their velocities is 2:3 then the ratio of their raddi is ​

Answer 1

Dear Student,

◆ Answer -

r1/r2 = 3/4

● Explanation -

For two spheres, ratio of kinetic energies is -

KE1/KE2 = (1/2 mv1²) / (1/2 mv2²)

KE1/KE2 = (d × 4/3 πr^3 × v1²) / (d × 4/3 πr^3 × v1²)

KE1/KE2 = (r1^3 × v1²) / (r2^3 × v2²)

(r1/r2)^3 = KE1/KE2 × (v2/v1)^2

(r1/r2)^3 = 108/576 × (3/2)^2

(r1/r2)^3 = 27/64

r1/r2 = 3/4

Therefore, ratio of their radii is 3/4.

Hope this helps you..

Answer 2

Answer:

The ratio of their raddi is 3:4 .

Explanation:

Given,

KE1:KE2 = 108:586

So, KE1 = 108 and KE2 = 576.

V1:V2 = 2:3

So, V1= 2 and V2 = 3.

As we know that how to find the ratio of their radii. First of all we have to use the formula of kinetic energy.

KE = 1/2 mv²

=> KE1/KE2 = 1/2 mv1² / 1/2 mv2²

=> KE1/KE2 = d × 4/3 πr1³ × v1² / 1/2 d × 4/3 πr2³ × v2²

=> KE1/KE2 = r1³ × v1² / r2³ × v2²

So,

(r1/r2)³ = KE1/KE2 × (v2/v1)²

=> (r1/r2)³ = 108/576 × (3/2)²

=> (r1/r2)³ = 27/64

=> (r1/r2) = 3/4

.°. (r1/r2) = 3/4

Therefore, the ratio of their raddi is 3/4.