Question on: WAEC Physics - 2011
The density P of a spherical ball of diameter d and mass m is given by
A
P = \(\frac{3m}{4 \pi d^3}\)
B
p = 4\(\pi md^3\)
C
p = \(\frac{6m}{\pi d^3}\)
D
p = \(\frac{3m}{2 \pi d^3}\)
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Correct Option: C
The density of an object is defined as mass per unit volume. For a sphere, the volume is given by the formula \(V = \frac{4}{3}\pi r^3\), where r is the radius. Since the diameter d is twice the radius (d = 2r), we can express the radius as \(r = \frac{d}{2}\). Substituting this into the volume formula, we get:
\(V = \frac{4}{3}\pi (\frac{d}{2})^3 = \frac{4}{3}\pi \frac{d^3}{8} = \frac{\pi d^3}{6}\)
Density (P) is mass (m) divided by volume (V): \(P = \frac{m}{V}\). Substituting the volume formula we derived:
\(P = \frac{m}{\frac{\pi d^3}{6}} = \frac{6m}{\pi d^3}\)
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