The bulk modulus of a spherical object is B. If it is subjected to uniform pressure P, the fractional decrease in radius is:
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The bulk modulus of a spherical object is B. If it is subjected to uniform pressure P, the fractional decrease in radius is:

G1 Physics · Accepted Answer

Step 1: For a small uniform compression, bulk modulus is B = −P/(ΔV/V). Step 2: Therefore, the magnitude of volumetric strain is |ΔV|/V = P/B. Step 3: A sphere has volume V = (4/3)πr³. Step 4: For a small radius change, differentiation gives ΔV/V ≈ 3Δr/r. Step 5: The fractional decrease in radius is −Δr/r = (1/3)(P/B) = P/(3B). Final answer: (D) P/(3B).