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:
- (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.
