Respuesta :
Answer:
The new period is approximately 3.93 × 10⁻⁷ h
Explanation:
The radius of the planet = 5 × 10⁶ m
The acceleration due to gravity on the planet, a = 10 m/s²
The period of the planet = 25 h
The centripetal force, [tex]F_c[/tex], is given by the following equation;
[tex]F_c = \dfrac{m \cdot v^2}{r}[/tex]
Where;
v = The linear speed
r = The radius
Therefore, for the apparent weight, W, of an object to be zero, we have;
The weight of the object = The centripetal force of the object
W = Mass, m × Acceleration due to gravity, a
∴ W = [tex]F_c[/tex]
Which gives;
[tex]m \times a = \dfrac{m \cdot v^2}{r}[/tex]
[tex]a = \dfrac{v^2}{r}[/tex]
∵ r = The radius of the planet
We have;
[tex]10 = \dfrac{v^2}{5 \times 10^6}[/tex]
v² = 10 × 5 × 10⁶
v = √(10 × 5 × 10⁶) ≈ 7071.07 m/s
The new frequency = Radius of the planet/(Linear speed component of rotation)
∴ The new frequency = 5 × 10⁶/(7071.07) = 707.107 revolutions per second
The new frequency = 707.107 × 60 × 60 = 2545585.2 revolutions per second
The new period = 1/Frequency ≈ 3.93 × 10⁻⁷ hour.
