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NEET
Exam
NEET
Subject
Physics
Chapter
Gravitation

NEET · Physics · Gravitation

(P(r)) is magnitude of physical quantity as a function of r...

(\mathrm{P}(\mathrm{r})) is magnitude of physical quantity as a function of r (distance from centre of spherical distribution of radius R). Match the following columns and select the correct option from the codes given below: (P(r)) is magnitude of physical quantity as a function of r (distance from centre of spherical distribution of radius
(P(r)) is magnitude of physical quantity as a function of r (distance from centre of spherical distribution of radius

Options

  1. AA-(S); B-(R); C-(Q); D-(P)
  2. B(A−(Q)\mathrm{A}-(\mathrm{Q}); B−(S)\mathrm{B}-(\mathrm{S}); C−(R)\mathrm{C}-(\mathrm{R}); D−(P)\mathrm{D}-(\mathrm{P}))
  3. C(A−(Q)\mathrm{A}-(\mathrm{Q}); B−(R)\mathrm{B}-(\mathrm{R}); C−(S)\mathrm{C}-(\mathrm{S}); D−(P)\mathrm{D}-(\mathrm{P}))
  4. D(A−(R)\mathrm{A}-(\mathrm{R}); B−(S)\mathrm{B}-(\mathrm{S}); C−(P)\mathrm{C}-(\mathrm{P}); D−(Q)\mathrm{D}-(\mathrm{Q}))

Correct answer

C. (A−(Q)\mathrm{A}-(\mathrm{Q}); B−(R)\mathrm{B}-(\mathrm{R}); C−(S)\mathrm{C}-(\mathrm{S}); D−(P)\mathrm{D}-(\mathrm{P}))

Step-by-step solution

Potential sphere V=−GM2R3(3R2−r2) for  r≤RV=−GMr for r>RShell V=−GMr for r≤RV=−GMr for r>R\begin{aligned} & V=-\frac{G M}{2 R^3}\left(3 R^2-r^2\right) \text{\text{ for } } r \leq R \\ & V=-\frac{G M}{r} \text{ for } r>R \\ & \text{Shell } V=-\frac{G M}{r} \text{ for } r \leq R \\ & V=-\frac{G M}{r} \text{ for } r>R \end{aligned}) Field sphereEg=GMR3.r for  r≤REg=GMr2 for  r>RShell Eg= zero for  r<REg=GMr2 for  r≥R\begin{aligned} & E_g=\frac{G M}{R^3} . r \text{\text{ for } } r \leq R \\ & E_g=\frac{G M}{r^2} \text{\text{ for } } r>R \\ & \text{Shell } E_g=\text{ zero\text{ for } } r < R \\ & E_g=\frac{G M}{r^2} \text{\text{ for } } r \geq R \end{aligned})
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