Question

A rigid rod is rotating at a constant angular speed about an axis that is perpendicular to one end of the rod. A small ball is fixed to the rod at a distance that is 12 cm from the axis. The centripetal force acting on this ball is 1.7 N. What would be the centripetal force that acts on the ball if the ball were fixed to the rod at a distance of 33 cm from the axis?

Answer 1

Fc₂ = 4.675 N

Step-by-step explanation:

r₁ = 12 cm = 0.12 m

Fc= 1.7 N

Fc = mV²/r = m w² r ( ∴ V= r w )

Fc = m w² r ----------------------- (1)

As angular speed (w) and mass are constant.

let m * w² = k ------------------(2)

Put equation (2) in equation (1).

⇒ Fc = m w² r = k * r ( ∴ m w² = k)

⇒ Fc =k * r ----------------------( 3)

⇒ Fc₁ =k * r₁ = 1.7 N

⇒ k = 1.7/ r = 1.7 / 0.12 N ( as r₁=0.12 m )

⇒ k = 14.17

Centripetal force hen the rod is fixed at 33 cm from the axis:

From equation ( 3 )

Fc₂ = k * r₂

Fc₂ = 14.17 * 0.33 N ( ∴ r₂ = 0.33 m)

Fc₂ = 4.675 N