A spherical object has bulk modulus B. It is subjected to a small uniform increase in pressure p. Find the fractional decrease in its radius.
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Question

A spherical object has bulk modulus B. It is subjected to a small uniform increase in pressure p. Find the fractional decrease in its radius.

G1 Physics · Accepted Answer

Step 1: Bulk modulus is B = −ΔP/(ΔV/V). For compressive pressure p, |ΔV|/V = p/B. Step 2: For a sphere, V = 4πR³/3. Step 3: For small changes, ΔV/V = 3ΔR/R. Step 4: Therefore magnitude of the fractional decrease in radius is |ΔR|/R = (1/3)(p/B). Final answer: p/(3B) (Option C).