Two particles of masses in the ratio 3:5 are moving in circular paths of radii in the ratio 4:7 with time periods in the ratio 4:5 . The ratio of their centripetal forces is

Options

A. `16/28`
B. `15/28`
C. `192/875`
D. `23/28`

Answer

B

Explanation

The centripetal force
`F=(mv^(2))/(r)=mromega^(2) " "therefore (F_1)/F_(2)=(m_1r_1omega_1^2)/(m_2r_2omega_2^2)`
`(m_(1))/(m_(2))=3/5,T_1/T_2=4/5,r_1/r_2=4/7 " "becauseomega =2pi//T" "thereforomega_1/omega_2=T_2/T_1=5/4`
Thus , `F_1/F_2=(m_1r_1omega_1^2)/(m_2r_2omega_2^1)=3/5xx4/7xx(5/4)^2=3/7xx5/4=15/28`