A spherical shell of mass m and radius R having uniform mass distribution over the surface. If inside the shell gravitational field at a distance R2 from center is a and outside field at distance is b, then the ratio (a+b)/b is
Question
A spherical shell of mass m and radius R having uniform mass distribution over the surface. If inside the shell gravitational field at a distance R2 from center is a and outside field at distance is b, then the ratio (a+b)/b is
Solution
The gravitational field inside a spherical shell of uniform mass distribution is zero. This is a result of the shell theorem. Therefore, the value of 'a' in this case is 0.
The gravitational field outside the shell at a distance R from the center is given by the formula for the gravitational field due to a point mass, as all the mass can be considered to be concentrated at the center. This is also a result of the shell theorem. The formula is:
b = GM/R^2
where G is the gravitational constant and M is the mass of the shell.
Therefore, the ratio (a+b)/b is (0 + GM/R^2) / (GM/R^2) = 1.
So, the ratio (a+b)/b is 1.
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