Question

The dependence of g on geographical latitude at sea level is given by `g = g_0(1 + betasin^2Phi)` where Φ is the latitude angle and β is a dimensionless constant. If Δg is the error in the measurement of g then the error in measurement of latitude angle is ______.

Options

• zero

• `DeltaPhi = (Deltag)/(g_0betasin(2Phi))`

• `DeltaPhi = (Deltag)/(g_0betacos(2Phi))`

• `DeltaPhi = (Deltag)/g_0`

Answer 1

The dependence of g on geographical latitude at sea level is given by `g = g_0(1 + betasin^2Phi)` where Φ is the latitude angle and β is a dimensionless constant. If Δg is the error in the measurement of g then the error in measurement of latitude angle is `underlinebb(DeltaPhi = (Deltag)/(g_0betasin(2Phi)))`.

Explanation:

`g = g_0(1 + betasin^2Phi)`

`(dg)/(dPhi) = g_0(2betasinPhi cosPhi)`

`(dg)/(g_0(betasin2Phi)) = dPhi`

or `(Deltag)/(g_0(betasin2Phi)) = DeltaPhi`