Q.

Acceleration due to gravity on the surface of the earth is g=GMR2. The gravitational constant G is exactly known. But percentage error in measurement of the mass of earth M and radius of the earth R are 1% and 2% respectively. The maximum percentage error in measurement of acceleration due to gravity on the surface of the earth is n%. The value of n is _________________

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answer is 5.

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Detailed Solution

∵ g=GMR2∴ Δgg=ΔMM+2ΔRRPercentage error in g isΔgg×100=ΔMM×100+2ΔRR×100=1+4=5%
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Acceleration due to gravity on the surface of the earth is g=GMR2. The gravitational constant G is exactly known. But percentage error in measurement of the mass of earth M and radius of the earth R are 1% and 2% respectively. The maximum percentage error in measurement of acceleration due to gravity on the surface of the earth is n%. The value of n is _________________