Gravitation - Result Question 18

18. Imagine a new planet having the same density as that of earth but it is 3 times bigger than the earth in size. If the acceleration due to gravity on the surface of earth is $g$ and that on the surface of the new planet is $g^{\prime}$, then

(a) $g^{\prime}=g / 9$

(b) $g^{\prime}=27 g$

(c) $g^{\prime}=9 g$

(d) $g^{\prime}=3 g$

[2005]

Show Answer

Answer:

Correct Answer: 18. (d)

Solution:

  1. (d) We know that

$g=\frac{G M}{R^{2}}=\frac{G(\frac{4}{3} \pi R^{3}) \rho}{R^{2}}=\frac{4}{3} \pi G R \rho$

$g$ depends on radius of the planet

$\frac{g^{\prime}}{g}=\frac{R^{\prime}}{R}=\frac{3 R}{R}=3[$ As G & $\rho$ are constants]

$\therefore g^{\prime}=3 g$

If the radius of a planet decreases by $n %$, keeping its mass unchanged, the acceleration due to gravity on its surface increases by $2 n %$

$ \begin{gathered} \frac{\Delta g}{g}=-\frac{2 \Delta R}{R} \\ \quad=-2(-n) \\ \quad=2 n % \end{gathered} $



NCERT Chapter Video Solution

Dual Pane