Resultant of two forces 3P and 2P is R . If first force is doubled then resultant is also doubled. a

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3-1.Vectors

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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 between the two forces is ........... $^o$

A

${60}$

B

$120$

C

${70}$

D

${180}$

Solution

(b) ${R^2} = {(3P)^2} + {(2P)^2} + 2 \times 3P \times 2P \times \cos \theta $…(i)

${(2R)^2} = {(6P)^2} + {(2P)^2} + 2 \times 6P \times 2P \times \cos \theta $…(ii)

by solving (i) and (ii), $\cos \theta = – 1/2$

$⇒$ $\theta = 120^\circ $

Standard 11

Physics

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