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  • The resultant of two forces 3P and 2P is R. If the first force is doubled, then the resultant is also doubled. The angle beween the forces isOption: 1</stro

The resultant of two forces 3P and 2P is R. If the first force is doubled, then the resultant is also doubled. The angle beween the forces is

Option: 1

120\degree


Option: 2

60\degree


Option: 3

180\degree


Option: 4

90\degree


Answers (1)

best_answer

As we learned

 From the triangle law of vector addition 

So using concept  

R^2=(3P)^2+(2P)^2+2\cdot (3P)\cdot (2P)\cdot \cos\theta

R^2=13P^2+12P^2cos\theta                           .....(1)

When the first force is doubled, the resultant is doubled

So, (2R)^2=(6P)^2+(2P)^2+2\cdot (6P)(2P)\cdot\cos\theta

\Rightarrow 4R^2=36P^2+4P^2+24P^2\cos\theta

\Rightarrow R^2=10P^2+6P^2\cos\theta                     .....(2)

Equating (1) and (2)

\Rightarrow 13P^2+12P^2\cos\theta=10P^2+6P^2\cos\theta

\Rightarrow 3P^2=-6P^2\cos\theta

\Rightarrow\cos\theta =-\frac{1}{2} \: or\: \theta=120\degree

Posted by

rishi.raj

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