First slide

Accuracy; precision of instruments and errors in measurements

Question

Acceleration due to gravity on the surface of the earth is $g = \frac{G M}{R^{2}}$ . 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 _________________

Easy

Solution

$∵ g = \frac{G M}{R^{2}}$
$∴ \frac{Δ g}{g} = \frac{Δ M}{M} + \frac{2 Δ R}{R}$
Percentage error in g is
$\frac{Δ g}{g} \times 100 = \frac{Δ M}{M} \times 100 + \frac{2 Δ R}{R} \times 100 = 1 + 4 = 5 %$

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