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

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5N, 37⁰ with x-axis

10N, 37⁰with x-axis

5N, 53⁰ with x-axis

10N, 53⁰with x-axis

answer is C.

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Detailed Solution

force exerted on m = mg
$g = | \vec{g} | = \sqrt{3^{2} + 4^{2}} = 5$
Angle made by $\vec{g}$ with x-axis = $\tan^{- 1} \frac{4}{3} = 53^{0}$ with x-axis
$∴ F = 2 \times 5 = 10 N, 53^{0} with x - axis$

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