If the radius of curvature of the path of two particles of same masses are in the ratio `1 : 2`, then in order to have same centripetal force, their velocity, should be in the ratio of

Options

A. `1:4`
B. `4:1`
C. `sqrt2:1`
D. `1:sqrt2`

Answer

D

Explanation

The centripetal force , `F=(mv^(2))/(r) therefore =(mv^(2))/(F)`,
` therefore r alpha v^(2) or v alpha sqrtr ` (If m and F are constant),
` therefore(v_(1))/(v_(2))=sqrt((v_(1))/(v^(2))=sqrt(1)/(2)`.