Question

The gravitational field at some point in space is $\overrightarrow{g}=3\hat{i}+4\hat{j}$ N/kg. The force exerted on a 2kg mass placed at that point is

• A. 5N,${53}^0$ with x-axis
• B. 5N,${37}^0$ with x-axis
• C. 10N,${53}^0$ with x-axis
• D. 10N,${37}^0$ with x-axis

Answer 1

The correct option is C 10N,${53}^0$ with x-axis

Given acceleration

$\overrightarrow{g}=3\hat{i}+4\hat{j}$ N/kg

$\therefore |\overrightarrow{g}|=\sqrt{3^2+4^2}=\sqrt{9+16}=\sqrt{25}$

$\therefore g=5$ N/kg

Thus, the force exerted by gravity on the a mass $m=2$ kg is be given by,

$F=ma$

Substituting $m=2$ kg and $a=g=5$ N/kg

$\therefore F=2\times 5$

$\therefore F=10$ N

Thus the force exerted by gravity has a magnitude of $10$ N, at an angle of ${53}^0$ with x-axis as shown in the figure