Gravitation - Result Question 19
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19. The density of a newly discovered planet 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 is R, the radius of the planet would be
======= ####19. The density of a newly discovered planet 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 is R, the radius of the planet would be
3e0f7ab6f6a50373c3f2dbda6ca2533482a77bed:content/english/neet-pyq-chapterwise/physics/gravitation/gravitation—result-question-19.md (a) $1 / 2 R$
(b) $2 R$
(c) $4 R$
(d) $1 / 4 R$
[2004]
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Answer:
Correct Answer: 19. (a)
Solution:
- (a) $g=\frac{G M}{R^{2}}$. Also, $M=\rho \times \frac{4}{3} \pi R^{3}$
$\therefore \quad g=G \frac{4}{3} \rho \pi R$.
At the surface of planet, $g_p=\frac{4}{3} G(2 \rho) \pi R^{\prime}$,
At the surface of the earth $g_e=\frac{4}{3} G \rho \pi R$
$g_e=g_p \Rightarrow \rho R=2 \rho R^{\prime} \Rightarrow R^{\prime}=R / 2$
