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JEE Advanced 2015Paper 2
Exam
JEE Advanced
Year
2015
Paper
Paper 2
Subject
Physics
Chapter
Mechanical Properties of Fluids

JEE Advanced 2015 · Paper 2 · Physics · Mechanical Properties of Fluids

A spherical body of radius R consists of a fluid of constant...

A spherical body of radius RR consists of a fluid of constant density and is in equilibrium under its own gravity. If P(r)P ( r ) is the pressure at r(r<R)r ( r < R ) , then the correct option(s) is (are)A spherical body of radius R consists of a fluid of constant density and is in equilibrium under its own gravity. If P

Options

  1. AP(r=0)=0P\left(r = 0\right) = 0
  2. BP(r=3R4)P(r=2R3)=6380\dfrac{P\left(r = \dfrac{3R}{4}\right)}{P\left(r = \dfrac{2R}{3}\right)} = \dfrac{63}{80}
  3. CP(r=3R5)P(r=2R5)=1621\dfrac{P\left(r = \dfrac{3R}{5}\right)}{P\left(r = \dfrac{2R}{5}\right)} = \dfrac{16}{21}
  4. DP(r=R2)P(r=R3)=2027\dfrac{P\left(r = \dfrac{R}{2}\right)}{P\left(r = \dfrac{R}{3}\right)} = \dfrac{20}{27}

Correct answer

B. P(r=3R4)P(r=2R3)=6380\dfrac{P\left(r = \dfrac{3R}{4}\right)}{P\left(r = \dfrac{2R}{3}\right)} = \dfrac{63}{80}

Step-by-step solution


A spherical body of radius R consists of a fluid of constant density and is in equilibrium under its own gravity. If P
dE=dE =\left[P - \left(P + dP\right)\right]A<br><br >⇒ \dfrac{Gm}{{r}^{2}}dm = - (dP)A\left(dP\right)A
⇒∫0PdP=−∫ErGMr3R34ar2drρr2(4πr2)⇒ \mathop{∫}_{0}^{P}dP = - \mathop{∫}_{E}^{r}\dfrac{G\dfrac{M{r}^{3}}{{R}^{3}}4a{r}^{2}drρ}{{r}^{2}\left(4\pi{r}^{2}\right)}<br><br >∴ P = \dfrac{GρM}{2R}(1−r2R2)\left(1 - \dfrac{{r}^{2}}{{R}^{2}}\right)
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