00:01
Hello guys, i'm here to solve this problem.
00:02
So calculate the energy you get if the sun is powered by gravitational contraction and calculate how long you can power the sun that way.
00:13
So first of all we make the diagram.
00:14
So suppose the mass of the earth is m and we consider a small particle.
00:21
Suppose it's a small particle and so the radius of this circle.
00:27
So it is the radius which is equal to i.
00:30
Capital r and it is a radius which is smaller now we consider the small particle which is d and the mass of this circle is m so m and r the mass of the mass and radius of the sun so the capital m and r is the mass of the sun and r is the mass of the sun assuming the sun be of a uniform density so what is the sun of uniform density del so the sun uniform density is the to m divide by because the density is equal to mass upon volume so what is the volume of this circle which is 4 upon 3 4 by 3 pi r square so pi r q it's equation 1 because we know that the density is equal to mass upon volume so that's why we use this equation here now construct a cell of thickness d r so we construct a cell which is the thickness of this cell is dr, 8 distance of r, and the distance is r from the center.
01:38
And the gravity, so we can say that the gravitational potential energy.
01:42
So what is the gravitational potential energy? means d is equal to minus g and the integration from 0 to r.
01:51
And the potential energy defined by m, small r multiplied by, by, 4, by, r, or, square d r and multiply by the density divided by r so it is the equation because we know that the u is equal to u is equal to minus g m1 divided by r so we use this equation for calculate the value of d u so where for pi r squared d r multiply del it is the mass of the cell mass of the cell so m1 and m2, m1 is the mass of the earth and m2 is the mass of the cell which is 4 pi r squared d r multiplied density because mass is equal to, if you know that mass is equal to density multiplied volume...