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प्रश्न
Solve the following problem.
Calculate the value of acceleration due to gravity on the surface of Mars if the radius of Mars = 3.4 × 103 km and its mass is 6.4 × 1023 kg.
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उत्तर
Given: M = 6.4 × 1023 kg, R = 3.4 × 103 km = 3.4 × 106 m,
To find: Acceleration due to gravity on the surface of the Mars (gM)
Formula: g = `"GM"/"R"^2`
Calculation: As, G = 6.67 × 10-11 Nm2/kg2
From formula,
`"g"_"M" = (6.67 xx 10^-11 xx 6.4 xx 10^23)/(3.4 xx 10^6)^2 = (6.67 xx 6.4)/(3.4 xx 3.4)`
= antilog{log(6.67) + log(6.4) - log(3.4) - log(3.4)}
= antilog{(0.8241) + (0.8062) - (0.5315) - (0.5315)}
= antilog {0.5673}
= 3.693 m/s2
Acceleration due to gravity on the surface of Mars is 3.693 m/s2.
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