Two forces 3,N and 2, N are at an angle θ such that resultant is R . first force is now increased t

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3-1.Vectors

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Two forces $3\,N$ and $2\, N$ are at an angle $\theta$ such that the resultant is $R$. The first force is now increased to $ 6\,N$ and the resultant become $2R$. The value of is ....... $^o$

A

$30$

B

$60$

C

$90$

D

$120$

Solution

(d) $A = 3N$, $B = 2N$ then $R = \sqrt {{A^2} + {B^2} + 2AB\cos \theta } $

$R = \sqrt {9 + 4 + 12\cos \theta } $ …$(i)$

Now $A = 6N$, $B = 2N$ then

$2R = \sqrt {36 + 4 + 24\cos \theta } $ …$(ii)$

from $(i)$ and $(ii)$ we get $\cos \theta = – \frac{1}{2}$

$\therefore $ $\theta = 120^\circ $

Standard 11

Physics

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(AIPMT-2001)