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JIPMER 2007
Exam
JIPMER
Year
2007
Subject
Physics
Chapter
Gravitation

JIPMER 2007 · Physics · Gravitation

Imagine a new planet having the same density as that of earth but...

Imagine a new planet having the same density as that of earth but it is 33 times bigger than the earth in size. If the acceleration due to gravity on the surface of earth is gg and that on the surface of the new planet is g′g^{\prime}, then

Options

  1. Ag′=3gg^{\prime}=3 g
  2. Bg′=g9g^{\prime}=\frac{g}{9}
  3. Cg′=9gg^{\prime}=9 g
  4. Dg′=27gg^{\prime}=27 g

Correct answer

A. g′=3gg^{\prime}=3 g

Step-by-step solution

The acceleration due to gravity on the new planet can be found using the relation g=GMR2...(i)g=\frac{G M}{R^2}...(i) but M=43πR3ρ,ρM=\frac{4}{3} \pi R^3 \rho, \rho being density. Thus, Eq. (i) becomes ∴g=G×43πR3ρR2\therefore g=\frac{G \times \frac{4}{3} \pi R^3 \rho}{R^2} =G×43πRρ=G \times \frac{4}{3} \pi R \rho ⇒g∝R∴g′g=R′R⇒g′g=3RR=3⇒g′=3g\begin{array}{ll}\Rightarrow & g \propto R \\ \therefore & \frac{g^{\prime}}{g}=\frac{R^{\prime}}{R} \\ \Rightarrow & \frac{g^{\prime}}{g}=\frac{3 R}{R}=3 \\ \Rightarrow & g^{\prime}=3 g\end{array}
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