Question

If the resultant of 3p and 4p is a force 5p, then the angle between 3p and 5p is:

• A. $si{n}^{-1}\left(\frac{3}{5}\right)$
• B. $si{n}^{-1}\left(\frac{4}{5}\right)$
• C. ${90}^o$
• D. None of these

Answer 1

The correct option is B $si{n}^{-1}\left(\frac{4}{5}\right)$

$Q=\frac{Rsin\alpha }{sin(\alpha +\beta )}$

Also, $(5P{)}^2=(4P{)}^2+3(P{)}^2+2(4P\left)\right(3P\left)cos\right(\alpha +\beta )$

$\Rightarrow 25P^2=16P^2+9P^2+24P^{2}cos(\alpha +\beta )$

$\Rightarrow 24P^{2}cos(\alpha +\beta )=0$

$\Rightarrow cos(\alpha +\beta )=0$

$\Rightarrow \alpha +\beta ={90}^0$

Now, $4P=\frac{5Psin\alpha }{sin{90}^o}$

$\Rightarrow sin\alpha =\frac{4}{5}$

$\Rightarrow \alpha =si{n}^{-1}\left(\frac{4}{5}\right)$

Hence, option B is correct.