Answer:
1.26 s
Explanation:
Draw a free body diagram. There are three forces: weight force mg pulling down, vertical tension component Tᵧ pulling up, and horizontal tension component Tₓ pulling radially.
Sum of forces in the vertical direction:
∑F = ma
Tᵧ − mg = 0
Tᵧ = mg
Sum of forces in the centripetal direction:
∑F = ma
Tₓ = m v² / r
Tension force must be in the same direction as the string, so:
Tₓ / Tᵧ = 75 / 40
40 Tₓ = 75 Tᵧ
40 m v² / r = 75 mg
8 v² / r = 15 g
v = √(15gr / 8)
Plugging in values:
v = √(15 × 10 m/s² × 0.75 m / 8)
v = 3.75 m/s
The circumference of the path is:
C = 2πr
C = 2π (0.75 m)
C = 4.71 m
So the period is:
t = C / v
t = 4.71 m / 3.75 m/s
t = 1.26 s
Round as needed.