A solid sphere of radius 4cm has a mass of 64kg. What will be the mass of a shell of the same metal whose internal and external radii are 2cm and 3cm respectively?
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Correct Answer: Option A
Explanation:
\(\frac{1\sqrt{3}}{(\frac{1}{2})^2}\)
= \(\frac{4}{\sqrt{3}}\)
= \(\frac{\sqrt{3}}{\sqrt{3}}\)
= \(\frac{4\sqrt{3}}{\sqrt{3}}\)
m = 64kg, V = \(\frac{4\pi r^3}{3}\)
= \(\frac{4\pi(4)^3}{3}\)
= \(\frac{256\pi}{3}\) x 10-6m3
density(P) = \(\frac{\text{Mass}}{\text{Volume}}\)
= \(\frac{64}{\frac{256\pi}{3 \times 10^{-6}}}\)
= \(\frac{64 \times 3 \times 10^{-6}}{256}\)
= \(\frac{3}{4 \times 10^{-6}}\)
m = PV = \(\frac{3}{4 \pi \times 10^{-6}}\) x \(\frac{4}{3}\) \(\pi\)[32 - 22] x 10-6
\(\frac{3}{4 \times 10^{-6}}\) x \(\frac{4}{3}\) x 5 x 10-6
= 5kg
\(\frac{1\sqrt{3}}{(\frac{1}{2})^2}\)
= \(\frac{4}{\sqrt{3}}\)
= \(\frac{\sqrt{3}}{\sqrt{3}}\)
= \(\frac{4\sqrt{3}}{\sqrt{3}}\)
m = 64kg, V = \(\frac{4\pi r^3}{3}\)
= \(\frac{4\pi(4)^3}{3}\)
= \(\frac{256\pi}{3}\) x 10-6m3
density(P) = \(\frac{\text{Mass}}{\text{Volume}}\)
= \(\frac{64}{\frac{256\pi}{3 \times 10^{-6}}}\)
= \(\frac{64 \times 3 \times 10^{-6}}{256}\)
= \(\frac{3}{4 \times 10^{-6}}\)
m = PV = \(\frac{3}{4 \pi \times 10^{-6}}\) x \(\frac{4}{3}\) \(\pi\)[32 - 22] x 10-6
\(\frac{3}{4 \times 10^{-6}}\) x \(\frac{4}{3}\) x 5 x 10-6
= 5kg