Question

When the angular frequency of the rotor in the experiment is increased the spring force increases there is no change in the orbital speed the radius of the orbit decreases the centripetal force increases by the same proportion

a) the spring force increases

b) there is no change in the orbital speed

c) the radius of the orbit decreases

d) the centripetal force increases by the same proportion

If an object in circular motion at radius r and speed v has its radius increased fourfold, for the same centripetal force, its speed would

a) remain the same

b) double

c) increase by a factor of 4

d) decrease by one-half

Answer 1

Centripetal force = mv²/r

m is the mass of the object, r is the radius, v is the velocity

Initial force = mv₁²/r₁

Now r₂ = 4r₁.....eq 1

Since the force remains the same hence,

mv₁²/r₁ = mv₂²/r₂

Using eq 1, we get

v₂ = 2*v₁

Hence option b is correct.