Two particles of the same mass m are moving in circular orbits because of force, given by
`F(r)=(-16)/(r)-r^(3)`
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 closet to :

Options

A. `10^(-1)`
B. `6xx10^(-2)`
C. `6xx10^(2)`
D. `3xx10^(-3)`

Answer

B

Explanation

As the particles moving in circular orbits ,so
`(mv^(2))/(R )=(16)/(R )+r^(2)`
Kinetic energy,`KE_(0)=(1)/(2)mv^(2)=(1)/(2)[16+r^(4)]`
For first particle,r=1,`K_(1)=(1)/(2)m(16+1)`
Similarly ,for second particle ,r=4 ,`k_(2)=(1)/(2)m(16+256)`
`therefore (K_(1))/(K_(2))=((16+1)/(2))/((16+256)/(2))=(17)/(272)=6xx10^(2)`