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
Answers
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:
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.