A radial force is F=br for ra. Find n if work done from r=0 to r=∞ is a²b/n + b/a.

Question

A radial force is F=br for r<a and F=b/r² for r>a. Find n if work done from r=0 to r=∞ is a²b/n + b/a.

G1 Physics · Accepted Answer

Step 1: Work is W=∫₀ᵃ br dr + ∫ₐ^∞ b/r² dr. Step 2: First part =b[a²/2]=ba²/2. Step 3: Second part =[−b/r]ₐ^∞=b/a. Step 4: Thus W=ba²/2+b/a and n=2.