Question

The mass of a person on earth is 80kg what will be the value of acceleration due to gravity on the moon and also the the mass of the person on moon if the person can jump to a height of 2m on earth how high can he jump on moon mass of moon is 7. 3 ×10^22kg and radius of moon is 1.75 ×10^6m/ s

Answer 1

g on earth = g
g on moon = g'
Weight on earth = 80 kg
mass × g of earth = 80 N
m g = 80 N
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g on moon = (1/6)th of g on earth
g' = (1/6) g
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g' = G M/R^2
= (6.75×10^-11)×(7.3×10^22)/(1.75×10^6)^2
= (49.275/3.0625) × 10^-1
= 1.608 m/sec^2
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g' = (1/6) g
1.6 = (1/6) g
g = 9.6 m/sec^2
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m g = 80
m × 9.6 = 80
m = 8.33 kg
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P.E = m g h
= 8.33 × 9.6 × 2
= 160 J
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As the potential energy of a person remains constant ;

P.E = m gm h'
160 = 8.33×1.6×h'
h' = 160/13.33
h' = 12 m (approx)
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Hence the person can jump 12m high on the surface of the moon.