Answer:
Option C
Explanation:
From mass conservation
ρ43πR3=ρK43πr3
⇒ R= K13r
∴ \triangle U= T\triangle A=T(K. 4\pi r^{2}-4\pi R^{2})
=T(K. 4\pi R^{2}K^{-\frac{2}{3}}-4\pi R^{2})
\triangle U=4\pi R^{2}T[K^{\frac{1}{3}}-1]
Putting the values, we get
10^{-3}=\frac{10^{-1}}{4\pi}\times 4\pi\times 10^{-4}[K^{-\frac{1}{3}}-1]
100=K^{\frac{1}{3}}-1
\Rightarrow K^{\frac{1}{3}}=100=10^{2}
Given that K= 10^{\alpha}
\therefore 10^{\frac{\alpha}{3}}=10^{2}
\Rightarrow \frac{\alpha}{3}=2
\Rightarrow \alpha=6