Question

Gravitational potential in a region is given by $v=-(x+y+z)$J/kg. Find the gravitational intensity at (2, 2 ,2)

• A. $(\hat{i}+\hat{j}+\hat{k})N/kg$
• B. 2$(\hat{i}+\hat{j}+\hat{k})N/kg$
• C. 3$(\hat{i}+\hat{j}+\hat{k})N/kg$
• D. 4$(\hat{i}+\hat{j}+\hat{k})N/kg$

Answer 1

The correct option is A $(\hat{i}+\hat{j}+\hat{k})N/kg$

We know formula $V=\overrightarrow{-u}.\overrightarrow{dr}$

or $G=\frac{-dv}{dr}$ where $h$ is gravitational field intensity, $V$ is gravitational potential and $dr$ is position vector.

given $V=-(x+y+z)$

We have to use partial derivative

$G_x=\frac{-\delta (-x)}{\delta x}\hat{i}$

$G_x=\hat{i}$

Similarly we get, $G_y=\hat{j}{h}_2=k$

now $G=\hat{i}+\hat{j}+\hat{k}$