Assuming that a neutron star has the same density as a neutron, calculate the mass in kilograms of a small piece of a neutron star the size of a spherical pebble with a radius of 0.30mm .

volume of sphere = (4/3)*pi*r^3

Plug into mass = volume x density
I assume you either have or can look up the other information.

Why did the neutron star go to the beach? Because it wanted to show off its stellar body!

Now, joking aside, to calculate the mass of a small piece of a neutron star, we'll need to use some physics. The density of a neutron is approximately 2.5 x 10^17 kilograms per cubic meter (kg/m^3).

To find the volume of the pebble, we can use the formula for the volume of a sphere:
V = (4/3) * π * r^3

Where:
V is the volume,
π is pi (approximately 3.14159),
and r is the radius.

Plugging in the values:
V = (4/3) * 3.14159 * (0.30mm)^3

Converting the radius to meters:
r = 0.30mm = 0.00030m

V = (4/3) * 3.14159 * (0.00030m)^3

Calculating the volume of the pebble:
V ≈ 1.129 x 10^-10 cubic meters

Now, to find the mass, we can multiply the volume by the density:
Mass = density * volume

Mass ≈ (2.5 x 10^17 kg/m^3) * (1.129 x 10^-10 m^3)

Calculating the mass:
Mass ≈ 2.8225 x 10^7 kilograms

So, the mass of a small piece of a neutron star the size of a spherical pebble with a radius of 0.30mm would be approximately 2.8225 x 10^7 kilograms. That's one heavy pebble!

To calculate the mass of a small piece of a neutron star with the same density as a neutron, we need to know the formula for the volume of a sphere and the density of a neutron.

The formula for the volume of a sphere is:
V = (4/3) * π * r^3

Given:
Radius (r) = 0.30 mm = 0.30 * 10^(-3) meters

Assuming the density of a neutron is approximately 1.0 x 10^17 kilograms per cubic meter, we can calculate the mass of the small piece of the neutron star.

Density (ρ) = 1.0 x 10^17 kg/m^3

Let's calculate the volume of the pebble first.
V = (4/3) * π * (0.30 * 10^(-3))^3
V ≈ 1.13 x 10^(-10) m^3

Now that we know the volume of the pebble, we can calculate its mass using the formula:
Mass (m) = Density (ρ) * Volume (V)

m = (1.0 x 10^17) * (1.13 x 10^(-10))
m = 1.13 x 10^7 kilograms

Therefore, the mass of a small piece of a neutron star with the same density as a neutron and a radius of 0.30 mm is approximately 1.13 x 10^7 kilograms.

To calculate the mass of the small piece of a neutron star, we need to use the formula for the volume of a sphere. Here are the steps to obtain the solution:

Step 1: Determine the volume of the pebble.
The volume of a sphere is given by the formula: V = (4/3) * π * r^3, where V is the volume and r is the radius.
Using the given radius of 0.30mm, we can calculate the volume as follows:
V = (4/3) * π * (0.30mm)^3

Step 2: Convert the radius to meters.
Since the formula requires the radius in meters, we need to convert 0.30mm to meters.
1 mm = 0.001 m, so 0.30mm = 0.30 * 0.001 = 0.0003 m.

Step 3: Calculate the volume of the pebble.
Now, we can substitute the radius value into the formula to find the volume:
V = (4/3) * π * (0.0003m)^3

Step 4: Find the density of a neutron star.
The question states that the neutron star has the same density as a neutron. The density of a neutron is approximately 2.1 x 10^17 kg/m^3.

Step 5: Calculate the mass of the pebble.
The mass (m) of an object is given by the formula: m = density * volume.
Substituting in the appropriate values, we get:
m = (2.1 x 10^17 kg/m^3) * V

Now you can proceed to calculate the mass by inserting the value of V from step 3 into the equation.