Answer:
<h3>The answer is option B</h3>Explanation:
The frequency of a wave can be found by using the formula
where
c is the velocity
From the question
wavelength = 0.39 m
c = 86 m/s
We have
We have the final answer as
<h3>200 Hz</h3>Hope this helps you
(a)
Here we want to find the gravitational force exerted on the particle at a distance of 3.7 m from the center of the sphere. Since the radius of the sphere is 1.9 m, we are outside the sphere, so we can use Newton's law of gravitation:
where
G is the gravitational constant
m = 8.3 kg is the mass of the particle
is the mass of the sphere
r = 3.7 m is the distance
Substituting into the formula, we find
(b)
Here we want to find the gravitational force exerted on the particle at a distance of 0.41 m from the center of the sphere. Since the radius of the sphere is 1.9 m, this time we are inside the sphere, so the formula for the gravitational force is different:
where
G is the gravitational constant
m = 8.3 kg is the mass of the particle
is the mass of the sphere
r = 0.41 m is the distance from the centre of the sphere
R = 1.9 m is the radius of the sphere
Substituting numbers into the formula, we find
(c)
The magnitude of the gravitational force on the particle when located inside the sphere can be found starting from Newton's law of gravitation:
(1)
where the only difference compared to the standard law is that M' is not the total mass of the sphere, but only the amount of mass of the sphere enclosed by the spherical surface of radius r centered in the center of the sphere.
The mass enclosed is
(2)
where is the density of the sphere and V' is the enclosed volume. We can rewrite the density of the sphere as ratio between mass of the sphere (M) and volume of the sphere:
(3)
where R is the radius of the sphere.
Substituting (3) into (2):
And substituting the last equation into (1), we find
which depends linearly on r.