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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 is measurement of acceleration due to gravity on the surface of the earth in n%. Find the value of n.

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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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