Question

When two equal forces are inclined at an angle $2\alpha$, their resultant is twice as great as when they act at an angle $2\beta$, then

• A. $cos\alpha =2cos\beta$
• B. $cos\alpha =2sin\beta$
• C. $cos\beta =2cos\alpha$
• D. $sin\beta =2cos\alpha$

Answer 1

The correct option is A $cos\alpha =2cos\beta$

Let the magnitude of each force be P. Then, $R_1$= Resultant of two equal forces each of magnitude P inclined at an angle $2\alpha =2Pcos\alpha$, and
$R_2$ = Resultant of two equal forces each of magnitude P inclined at an angle $2\beta =2Pcos\beta$.
It is given that, $R_1=2R_2$
$\Rightarrow 2Pcos\alpha =4Pcos\beta$
$\Rightarrow cos\alpha =2cos\beta$