Question

the gravitational field at some point in space is g= 3i+4j. the force exerted in a 2kg mass placed at that point is

Answer 1

$F=6\hat{i}+8\hat{j}\ N$ i.e. Magnitude of force $F=10\ N$ acting in direction

$\theta=53.13^{\circ}$ from the x-axis

Explanation:

Given:

• mass of the object, $m=2\ kg$

• gravitational field at the object, $g=3\hat{i}+4\hat{j}$

Now the force in magnitude is given as:

$\therefore F=m.g$

Gravitational field in vector form:

$F=2(3\hat{i}+4\hat{j})$

$F=6\hat{i}+8\hat{j}\ N$

Now the magnitude of gravitational field:

$g=\sqrt{3^3+4^2}$

$g=5\ m.s^{-2}$

Now the magnitude of force:

$F=2\times 5$

$F=10\ N$

Direction of the force:

$\theta=tan^{-1}\ \frac{8}{6}$

$\theta=53.13^{\circ}$ from the x-axis

TOPICS: magnitude of a vector, gravitational field

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