Eduprobe
Question:
Two particles of the same mass m are moving in circular orbits because of force, given by F(r) = 1/r - r³. The first particle is at a distance r = 1, and the second, at r = 4. The best estimate for the ratio of kinetic energies of the first and the second particle is closest to
6×102
3×10
6×10
10
Solution:
The correct option is B
6×10
The force is required for the circular motion of the body
Hence |F| = mv²/r
mv²/r = 1/r - r³
mv² = 1 - r⁴
K.E. = mv²/2 = (1 - r⁴)/2
Putting the value of r = 1 and r = 4 and taking the ratio
We get the ratio ≈ 6 × 10⁶