JEE MAIN - Physics (2020 - 7th January Evening Slot - No. 2)
The sum of two forces $$\overrightarrow P $$
and $$\overrightarrow Q $$
is $$\overrightarrow R $$
such that $$\left| {\overrightarrow R } \right| = \left| {\overrightarrow P } \right|$$
. The angle $$\theta $$ (in degrees) that the
resultant of 2$${\overrightarrow P }$$
and $${\overrightarrow Q }$$
will make with $${\overrightarrow Q }$$
is , ..............
Answer
90
Explanation
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$$\overrightarrow P + \overrightarrow Q = \overrightarrow R $$
$$ \Rightarrow $$ P2 + Q2 + 2PQcos$$\theta $$ = R2 = P2
[As $$\left| {\overrightarrow R } \right| = \left| {\overrightarrow P } \right|$$]
$$ \Rightarrow $$ 2Pcos$$\theta $$ + Q = 0
tan $$\alpha $$ = $${{2P\sin \theta } \over {Q + 2P\cos \theta }}$$ = $$\infty $$
$$ \Rightarrow $$ $$\alpha $$ = 90o
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