Question

If the earth were to cease rotating about its own axis. The increase in the value of $g$ in $C.G.S$. system at a place of latitude of ${45}^o$ will be

• A. $2.68$
• B. $1.69$
• C. $3.36$
• D. $0.34$

Answer 1

The correct option is B $1.69$

$\lambda ={45}^o$;
$R=6400\times {10}^{3}m$
$\omega =\frac{2\pi }{24\times 60\times 60}$
The value of acceleration due to gravity with latitude $\lambda$ due to rotation of earth is,
$g^{\prime }=g-R{\omega }^2{\cos }^2\lambda$
$g=g^{\prime }-R{\omega }^2{\cos }^2\lambda$
$=\frac{6400\times {10}^3}{2}\times {\left(\frac{2\times 3.14}{24\times 60\times 60}\right)}^2$

$=\frac{6400\times {10}^3\times 4\times 3.14\times 3.14}{2\times 24\times 60\times 60\times 24\times 60\times 60}$

$=16.89\times {10}^{-3}m/se{c}^2$
$=16.89\times {10}^{-1}cm/se{c}^2$
$=1.68cm/se{c}^2$