The surface area of a cube is:
S = 6l², making l the subject:
l = √(S/6)
While the volume is:
V = l³
If we substitute l to get:
V = (√(S/6))³
√(S/6) = ³√V
S/6 = (³√V)²
S = 6(³√V)² ⇒ 6V^(2/3)
Answer:
B
Explanation:
a force acting upon an object increases that objects acceleration
Answer:
θ’ = θ₀ / 2
we see that the resolution angle is reduced by half
Explanation:
The resolving power of a radar is given by diffraction, for which we will use the Rayleigh criterion for the resolution of two point sources, they are considered resolved if the maximum of diffraction of one coincides with the first minimum of the other.
The first minimum occurs for m = 1, so the diffraction equation of a slit remains
a sin θ = λ
in general, the diffraction patterns occur at very small angles, so
sin θ = θ
θ = λ / a
in the case of radar we have a circular aperture and the equation must be solved in polar coordinates, which introduces a numerical constant.
θ = 1.22 λ /a
In this exercise we are told that the opening changes
a’ = 2 a
we substitute
θ ‘= 1.22 λ / 2a
θ' = (1.22 λ / a) 1/2
θ’ = θ₀ / 2
we see that the resolution angle is reduced by half
Answer:
1. Potential hazard
2. Mining opportunity
Explanation:
The two reason, why astronomers are so interested in the discovery of additional Earth-approaching asteroids:
1. Potential hazard: We have proof that the dinosaurs got extinct because of an asteroid/comet strike on Earth. Also we have seen the effects of the Tunguska event and Chelyabinsk tragedy. These are enough to show us that asteroids can be very dangerous and wipe out the life from Earth.
2. Mining Opportunity: We have discovered a lot of asteroids which contains a lot of metal and precious elements. There can be a possibility of mining such asteroids in the future and reducing the burden on Earth.
To solve this problem we will use the concepts related to gravitational acceleration and centripetal acceleration. The equality between these two forces that maintains the balance will allow to determine how the rigid body is consistent with a spherically symmetric mass distribution of constant density. Let's start with the gravitational acceleration of the Star, which is
Here
Mass inside the orbit in terms of Volume and Density is
Where,
V = Volume
Density
Now considering the volume of the star as a Sphere we have
Replacing at the previous equation we have,
Now replacing the mass at the gravitational acceleration formula we have that
For a rotating star, the centripetal acceleration is caused by this gravitational acceleration. So centripetal acceleration of the star is
At the same time the general expression for the centripetal acceleration is
Where 
is the orbital velocity
Using this expression in the left hand side of the equation we have that
Considering the constant values we have that
As the orbital velocity is proportional to the orbital radius, it shows the rigid body rotation of stars near the galactic center.
So the rigid-body rotation near the galactic center is consistent with a spherically symmetric mass distribution of constant density
