Question

If the acceleration due to gravity, $g$, is $10m/s^2$ at the surface of the earth (radius $6400km$), then at a height of $1600km$ the value of $g$ will be? (in $m/s^2$)

• A. $4$
• B. $5$
• C. $7.5$
• D. $2.5$

Answer 1

The correct option is B $5$

The expression for value of $g$ at some height is as follows $g^1=g(1-\frac{2h}{R})$. Here $g^1$ is the value of acceleration to gravity $h$ is height $R$ is radius. It is given in problem that acceleration due to gravity is $10$ meter per should square of the surface of the earth (radius $6400km$) we have to calculate value of acceleration at height $1600km$

$g^1=g(1-\frac{2h}{R})$

Put $g=10$ meter per second square

$R=6400km$ and $h=1600km$

$g^1=10(1-\frac{2(1600\times 1000km)}{6400km})$

$g^1=5$

Value of $g^1=5m/s^2$.