Question

The gravitational field in a region is given by $\overrightarrow{E_g}$$=5\hat{i}+12\hat{j}$N/Kg, then the magnitude of the gravitational force acting on a particle of mass 2 Kg. placed at the origin, will be:

• A. zero
• B. $13N$
• C. $26N$
• D. $75N$

Answer 1

Answer: (C)

$26N$

Gravitation field is given as $\overrightarrow{E_g}=5\hat{i}+12\hat{j}$ N/Kg
Since, we need the magnitude of the gravitational force, first we find the magnitude of gravitational field.
i.e $E_g=\sqrt{5^2+{12}^2}=\sqrt{25+144}=\sqrt{169}=13$ N/Kg
Gravitational force is given by:
$F_g=m{E}_g=2\left(13\right)=26$ N