Question

# One of the two forces is double and the other resultant is equal to the greater force. The angle between then is

A
cos1(1/2)
B
cos1(1/2)
C
cos1(1/4)
D
cos1(1/4)

Solution

## The correct option is D $$cos^{-1} (-1/4)$$Let the smaller force is $$F$$so bigger force is  $$2F$$resultant $$(R)=2F$$$${R^2} = {F^2} + {\left( {2F} \right)^2} + 2 \times F \times 2F\cos \left( x \right)$$  (its a formula)$$\begin{array}{l} 4{ F^{ 2 } }={ F^{ 2 } }+4{ F^{ 2 } }+4{ F^{ 2 } }\cos \left( x \right) \\ 4{ F^{ 2 } }\cos \left( x \right) ={ F^{ 2 } } \\ \cos \left( x \right) =\frac { { -1 } }{ 4 } \\ x={ \cos ^{ -1 } }\left( { \frac { { -1 } }{ 4 } } \right) \end{array}$$$$\therefore$$ Option $$D$$ is correct.Physics

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