Laws of Motion - Result Question 27

27. Three forces acting on a body are shown in the figure. To have the resultant force only along the $y$ - direction, the magnitude of the minimum additional force needed is:

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(a) $0.5 N$

(b) $1.5 N$

(c) $\frac{\sqrt{3}}{4} N$

(d) $\sqrt{3} N$

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Answer:

Correct Answer: 27. (a)

Solution:

  1. (a) The components of $1 N$ and $2 N$ forces along $+x$-axis $=1 \cos 60^{\circ}+2 \sin 30^{\circ}$

$=1 \times \frac{1}{2}+2 \times \frac{1}{2}=\frac{1}{2}+1=\frac{3}{2}=1.5 N$

The component of $4 N$ force along $-x$-axis

$=4 \sin 30^{\circ}=4 \times \frac{1}{2}=2 N$.

Therefore, if a force of $0.5 N$ is applied along $+x$ axis, the resultant force along $x$-axis will become zero and the resultant force will be obtained only along $y$-axis.