Consider a planet in some

Question:

Consider a planet in some solar system which has a mass double the mass of earth and density equal to the average density of earth. If the weight of an object on earth is W, the weight of the same object on that planet will be:

  1. $2 \mathrm{~W}$

  2. $\mathrm{W}$

  3. $2^{\frac{1}{3}} \mathrm{~W}$

  4. $\sqrt{2} \mathrm{~W}$


Correct Option: , 3

Solution:

Density is same

$\mathrm{M}=\frac{4}{3} \pi \mathrm{R}^{3} \rho, 2 \mathrm{~m}=\frac{4}{3} \pi \mathrm{R}^{13} \rho$

$R^{\prime}=2^{1 / 3} R$

$\omega=\frac{\mathrm{GMm}}{\mathrm{R}^{2}}$

$\omega_{2}=\frac{\mathrm{G} 2 \mathrm{Mm}}{\mathrm{R}^{\prime 2}}$

$\omega_{2}=2^{1 / 3} \omega$

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