Question

If the radii of circular paths of two particles of same masses are in the ratio of 1:2, then in order to
a constant centripetal force, their velocities should be in the ratio of
a) 1:4
b) 4:1
c) 1:2
d) 2:1​

Answer 1

Answer:

ratio of velocity = 1:√2

Explanation:

let the radii be x and 2x. and v and u are velocity

centripetal force = mv^2/r

F1 = mv^2/x and

F2= mu^2/2x

as centripetal force is contant so,

F1=F2

=> mv^2/x = mu^2/2x

=> v^2 = u^2/2

=> (v/u)^2=1/2

=> v/u= 1/√2

so, ratio of velocity is 1:√2 respectively with raddi. 1:2.