First slide

Errors

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 percentage error in measurement of acceleration due to gravity on the surface of the earth is

Moderate

A

2%
B

5%
C

3%
D

7%

Solution

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

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