Two bodies having masses `10kg` and `5kg` are moving in concentric orbits of radii 4 and 8 such that their time periods are the same. Then the ratio of their centripetal accelerations is

Options

A. `(1)/(2)`
B. 2
C. 8
D. `(1)/(8)`

Answer

A

Explanation

`(2pir_(1))/(v_(1))=(2pir_(2))/(v_(2))rArr (v_(1))/(v_(2))=(r_(1))/(r_(2))=(1)/(2)`
`(v_(1)^(2)//r_(1))/(v_(2)^(2)//r_(2))=((v_(1))/(v_(2)))^(2).((r_(2))/(r_(2)))=(1)/(4).2=(1)/(2)`
Alternate method `(a_(1))/(a_(2))=(omega^(2)r_(1))/(omega^(2)r_(2))=(r_(1))/(r_(2))=(4)/(8)=(1)/(2)`