Question

Consider a spherical shell of mass density ?m = (A/r) exp[ -(r/R)2], where A = 4 x 104 kg m-2. The inner and outer shell radii are 3R and 4R respectively where R = 6 x 106. Find the inward gravitational acceleration on a particle of mass mp at a position of 4R. The spherical di erent is dV = r2 dr sin? d? d?.

A) 9.00 m/s2

B) 2.36 m/s2

C) 9.3 m/s2

D) 2.3 m/s2

E) 3.00 m/s2

Answer 1

The answer is C) 9.3 m/s2

I had to assume the mass density as (A/r) exp[+(r/R)2]. Otherwise with a negative exponential the answer comes out to be of the order of 10^(-11).