First slide

Acceleration due to gravity and its variation

Question

If the mass of the planet is 10% less than that of earth and radius of the planet is 20% greater than that of earth then the weight of 40kg person on that planet is

Easy

A

10 kg wt
B

25 kg wt
C

40 kg wt
D

60 kg wt

Solution

$R a d i u s i n c r e a s e d b y 20 % = R_{P} = R_{e} + 20 % R_{e} = = R_{e} + \frac{20}{100} R_{e} = R_{e} + 0.2 R_{e} = 1.2 R_{e} M a s s d e c r e a s e d b y 10 % = M_{P} = M_{e} - 10 % M_{e} = = M_{e} - \frac{10}{100} M_{e} = M_{e} - 0.1 M_{e} = 0.9 M_{e} g = \frac{G M}{R^{2}} \Rightarrow g α \frac{M}{R^{2}} \Rightarrow \frac{g_{P}}{g_{e}} = \frac{M_{P}}{M_{e}} {(\frac{R_{e}}{R_{P}})}^{2} = \frac{0.9 M_{e}}{M_{e}} {(\frac{R_{e}}{1.2 R_{e}})}^{2} = \frac{0.9}{1.44} = 0.625 \Rightarrow g_{P} = 0.625 g_{e} \Rightarrow W_{P} = 0.625 m g_{e} \Rightarrow W_{P} = 0.625 \times 40 g_{e} = 25 k g w t$

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