Question

The centripetal force of a body moving in a circular path, if speed is made half and radius is made four times the original value, will ____________.

Options

• increase by `16/15` times

• decrease by `15/16` times

• decrease by `8/15` times

• increase by `8/15` times

Answer 1

The centripetal force of a body moving in a circular path, if speed is made half and radius is made four times the original value, will decrease by `15/16` times.

Explanation:

`"Centripetal force," Fcp =("mv"^2)/r`

`"Changed centripetal force," F'cp = (m(v//2)^2)/(4r)`

`= ("mv"^2)/16r = (Fcp)/16`

`"i.e., decrease in "Fcp = Fcp - F'cp = (1-1/16) Fcp`

`= 15/16 Fcp`