Question

A ball of mass 100g is attached to the end of a string and is swung in a circle of radius 100cm at a constant velocity of 200cm/s. While in motion the string is shortened to 50cm. Calculate: (i) the new velocity of the motion. (ii) the new period of the motion. (4 marks)​

Answer 1

(i) 400 cm/s

(ii) π/4 s ≈ 0.8 s

Step-by-step explanation:

(i) Angular momentum is conserved.

m₁ v₁ r₁ = m₂ v₂ r₂

v₁ r₁ = v₂ r₂

(200 cm/s) (100 cm) = v (50 cm)

v = 400 cm/s

(ii) The period is the circumference divided by the velocity.

T = 2π r / v

T = 2π (50 cm) / (400 cm/s)

T = π/4 seconds

T ≈ 0.8 seconds