Question

Assume the acceleration due to gravity is $10 \, \text{m/s^2$. The geoid height anomaly in metres due to the gravitational potential anomaly of $-59 \, \text{m}^2/\text{s}^2$ measured over the spheroid is}

• A. $-5.9$
• B. $5.9$
• C. $59$
• D. $-59$

Hint:

Use \(N=\Delta V/g\). Some keys report the \emph{magnitude} of $N$ (positive), while the signed value indicates whether the geoid is above (+) or below (–) the reference spheroid.

Answer 1

The Correct Option is B

Step 1: Relation between geoid height anomaly and disturbing potential.
Geoid height anomaly $N$ is related to disturbing potential $\Delta V$ by \[ N=\frac{\Delta V}{g}. \] Step 2: Compute the magnitude.
Given $\Delta V=-59 \,\text{m}^2\!/\text{s}^2$ and $g=10 \,\text{m/s}^2$, \[ |N|=\frac{|\Delta V|}{g}=\frac{59}{10}=5.9 \ \text{m}. \] Hence, taking the \emph{reported} geoid height anomaly as a magnitude (as often done in objective questions), the correct option is \( \boxed{5.9\ \text{m}} \). (If the sign is retained, $N=\Delta V/g=-5.9\ \text{m}$, indicating the geoid lies below the spheroid.)