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NEET 2004
Exam
NEET
Year
2004
Subject
Physics
Chapter
Gravitation

NEET 2004 · Physics · Gravitation

The density of a newly discovered plant is twice that of earth. The...

The density of a newly discovered plant is twice that of earth. The acceleration due to gravity at the surface of the planet is equal to that at the surface of the earth. If the radius of the earth RR, the radius of the planet would be:

Options

  1. A2R2 R
  2. B4R4 R
  3. C14R\frac{1}{4} R
  4. D12R\frac{1}{2} R

Correct answer

D. 12R\frac{1}{2} R

Step-by-step solution

We know that: g=GMR2=G43πR3ρR2=43\piGρR\begin{aligned}g=\frac{G M}{R^2}& =\frac{G \frac{4}{3} \pi R^3 \rho}{R^2}\\ & =\frac{4}{3} \piG \rho R \end{aligned}New according to thequestionthe questiongplanel =gearh ⇒Rplanel =Rearth 2\begin{aligned}g_{\text{planel }} & =g_{\text{earh }} \\ \Rightarrow \quad R_{\text{planel }} & =\frac{R_{\text{earth }}}{2} \end{aligned}$
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