The radius of the path of a body in uniform circular motion is doubled. The centripetal force needed, if its speed remains the same is

Question

The radius of the path of a body in uniform circular motion is doubled. The centripetal force needed, if its speed remains the same is (A) half as great as before (B) same as before (C) twice as great as before (D) four times as great as before.

Tardigrade Admin · Accepted Answer

Let centripetal force initially be F0 ⇒ F0=(m v2/R0) Now , F new =(m v2/(2 R0))=(F0/2)

Q. The radius of the path of a body in uniform circular motion is doubled. The centripetal force needed, if its speed remains the same is

half as great as before

same as before

twice as great as before

four times as great as before.

Let centripetal force initially be $F_{0}$
$\Rightarrow F_{0} = \frac{m v ^{2}}{R _{0}}$
$N o w, F_{n e w} = \frac{m v ^{2}}{( 2 R _{0} )} = \frac{F _{0}}{2}$

Q. The radius of the path of a body in uniform circular motion is doubled. The centripetal force needed, if its speed remains the same is

half as great as before

same as before

twice as great as before

four times as great as before.

Let centripetal force initially be F0​ ⇒F0​=R0​mv2​ Now,Fnew​=(2R0​)mv2​=2F0​​

Let centripetal force initially be $F_{0}$
$\Rightarrow F_{0} = \frac{m v ^{2}}{R _{0}}$
$N o w, F_{n e w} = \frac{m v ^{2}}{( 2 R _{0} )} = \frac{F _{0}}{2}$