First slide

Accuracy; precision of instruments and errors in measurements

Question

Acceleration due to gravity on the surface of the earth is $g = \frac{GM}{R^{2}}$ . 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 percent age error is measurement of acceleration due to gravity on the surface of the earth in n%. Find the value of n.

Moderate

Solution

$\begin{array}{l} ∵ g = \frac{GM}{R^{2}} \\ ∴ \frac{Δg}{g} = \frac{ΔM}{M} + \frac{2 ΔR}{R} \end{array}$
Percentage error in g is
$\begin{matrix} \frac{Δg}{g} \times 100 = \frac{ΔM}{M} \times 100 + \frac{2 ΔR}{R} \times 100 \\ = 1 + 4 = 5 % \end{matrix}$

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