an-astraonaut-weighs-3200N-on-a-planet-whose-mass-is-the-same-as-that-of-the-earth-but-whose-radius-is-half-that-of-the-earth-the-astronsut-weight-on-the-earth-is-what-

Question Number 104299 by aurpeyz last updated on 20/Jul/20

an astraonaut weighs 3200 N on a planet whose mass is the same as that of the earth but whose radius is half that of the earth . the astronsut weight on the earth is what ?

Answered by OlafThorendsen last updated on 20/Jul/20

g_{planet} = \frac{M_{planet} G}{R_{planet}^{2}}

g_{earth} = \frac{M_{earth} G}{R_{earth}^{2}}

\frac{g_{earth}}{g_{planet}} = \frac{M_{earth}}{M_{planet}} \times {(\frac{R_{planet}}{R_{earth}})}^{2}

but M_{planet} = M_{earth}

\Rightarrow \frac{g_{earth}}{g_{planet}} = {(\frac{R_{planet}}{R_{earth}})}^{2}

\Rightarrow \frac{g_{earth}}{g_{planet}} = {(\frac{1}{2})}^{2} = \frac{1}{4}

\Rightarrow Weight on earth =

Weight on the planet \times \frac{1}{4}

= \frac{3200}{4} = 800 N

(\approx 80 kg : correct for a

human being)

Answered by Dwaipayan Shikari last updated on 20/Jul/20

\frac{g}{g^{'}} = \frac{{(R + H)}^{2}}{R^{2}}

\frac{mg}{{mg}^{'}} = \frac{{(\frac{R}{2})}^{2}}{R^{2}}

\frac{mg}{{mg}^{'}} = \frac{1}{4}

\frac{mg}{3200} = \frac{1}{4}

mg = 800 N