JEE MAIN - Physics (2021 - 25th July Evening Shift - No. 9)
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 :
2W
W
$${2^{{1 \over 3}}}$$W
$$\sqrt 2 $$W
Explanation
Density is same
$$M = {4 \over 3}\pi {R^3}\rho ,2m = {4 \over 3}\pi R{'^3}\rho $$
$$R' = {2^{1/3}}R$$
$$\omega = {{GMm} \over {{R^2}}}$$
$${\omega _2} = {{G2Mm} \over {R{'^2}}}$$
$${\omega _2} = {2^{1/3}}\omega $$
$$M = {4 \over 3}\pi {R^3}\rho ,2m = {4 \over 3}\pi R{'^3}\rho $$
$$R' = {2^{1/3}}R$$
$$\omega = {{GMm} \over {{R^2}}}$$
$${\omega _2} = {{G2Mm} \over {R{'^2}}}$$
$${\omega _2} = {2^{1/3}}\omega $$
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