The change in the centripetal force of a body moving in a circular path , if speed is made half and radius is made 4 times the origenal value , will

Options

A. increacese by `(16)/(15)`
B. decrease by `(15)/(16)`
C. decrease by `(8)/(15)`
D. increase by `(8)/(15)`

Answer

B

Explanation

`(F_(2))/(F_(1))=(v_(2))/(v_(1))^(2)xx(r_(1))/r_(2)`
`=(1)/(4)xx(1)/(4)=(1)/(16)`
`(F_(2))/(F_(1)-1=(1)/(16)-1`
`(F_(2)-F_(1))/(F_(1))=(1-16)/(16)=(-15)/(16)`
`(DeltaF)/(F_(1))=(-15)/(16)`.