Question

An object of mass 50 g moves
uniformly along a circular orbit with
an angular speed of 5 rad/s. If the
centripetal force acting on the
particle is 6.25N , the linear speed of
the particle will be​

Answer 1

Answer:

The linear speed of the particle will be 25 m/s.

Explanation:

The mass of the object, m = 50 g = 0.05 Kg

The angular speed of the object, ω = 5 rad/s

The centripetal force acting on the object, F = 6.25 N

The equation to find centripetal force is given as:

F = mv² / r  → (1)

Where v is the linear velocity of the object and r is the radius of the circular path followed by the object.

First, we need to find the radius of the circular path. For that, we use the equation v = rω. Substituting this in equation (1),

 F = mr²ω² / r

 F = mrω²

∴ r = F / mω²

  r = 6.25 / (0.05 × 5²)

  r = 5 m

Now we can substitute this value of r in equation (1) to find the linear velocity.

(1) ⇒ v² = Fr / m

            = (6.25 × 5) / 0.05

       v² = 625

     ∴ v = √625

        v = 25 m/s