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JEE Main
Exam
JEE Main
Subject
Physics
Chapter
Mechanical Properties of Solids

JEE Main · Physics · Mechanical Properties of Solids

The bulk modulus of a spherical object is B . If it is subjected to...

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

Options

  1. ApB\dfrac{p}{B}
  2. BB3p\dfrac{B}{3p}
  3. C3pB\dfrac{3p}{B}
  4. Dp3B\dfrac{p}{3B}

Correct answer

D. p3B\dfrac{p}{3B}

Step-by-step solution

V=Volumeofsphere=43\pir3V = Volumeofsphere = \dfrac{4}{3}\pir^{3}
⇒∆VV=3∆rr⇒ \dfrac{∆ V}{V} = 3\dfrac{∆ r}{r}
also, bulk modulus, B=∣−p(∆VV)∣B = \left|\dfrac{- p}{\left(\dfrac{∆ V}{V}\right)}\right|
\left|- \dfrac{∆ V}{V}\right| = \dfrac{p}{B}<br/><br/>3\dfrac{\Deltar}{r} = \dfrac{p}{B}<br/><br/>\dfrac{\Deltar}{r} = \dfrac{p}{3B}
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