NEET-XII-Physics
11: Gravitation
- #4Consider a planet in some solar system which has a mass double the mass of the earth and density equal to the average density of the earth. An object weighing W on the earth will weight
(a) W
(b) 2 W
(c) W/2
(d) 21/3 W at the planet.digAnsr: dAns : (d) 21/3 W at the planet
The weight of the object on the Earth is `` W=m\frac{G{M}_{e}}{{{R}_{e}}^{2}}``.
Here, m is the actual mass of the object; Me is the mass of the earth and Re is the radius of the earth.
Let Rp be the radius of the planet.
Mass of the planet, `` {M}_{p}=2{M}_{e}``
If `` \rho `` is the average density of the planet then
`` \frac{4}{3}\pi {{R}_{p}}^{3}\times \rho =2\times \left(\frac{4}{3}\pi {{R}_{e}}^{3}\times \rho \right)``
`` \Rightarrow {R}_{p}={\left(2\right)}^{\frac{1}{3}}{R}_{e}``
Now, weight of the body on the planet is given by
`` {W}_{p}=m\left(\frac{G{M}_{p}}{{{R}_{p}}^{2}}\right)=m\left(\frac{2G{M}_{e}}{{2}^{{\displaystyle \frac{2}{3}}}{{R}_{e}}^{2}}\right)``
`` \Rightarrow {W}_{p}={2}^{\frac{1}{3}}\times m\left(\frac{G{M}_{e}}{{{R}_{e}}^{2}}\right)``
`` \Rightarrow {W}_{p}={2}^{\frac{1}{3}}\times W``
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