Two forces of magnitude $P$ & $Q$ acting at a point have resultant $R$. The resolved  part of $R$ in the direction of $P$ is of magnitude $Q$. Angle between the forces is :

  • A

    $2{\sin ^{ - 1}}\left( {\frac{P}{{2Q}}} \right)$

  • B

    $2{\sin ^{ - 1}}\left( {\frac{P}{{2Q}}} \right)^{\frac{1}{2}}$

  • C

    $2{\cos ^{ - 1}}\left( {\frac{P}{{2Q}}} \right)$

  • D

    $2{\cos ^{ - 1}}\left( {\frac{P}{{2Q}}} \right)^{\frac{1}{2}}$

Similar Questions

Which of the four arrangements in the figure correctly shows the vector addition of two forces $\overrightarrow {{F_1}} $ and $\overrightarrow {{F_2}} $ to yield the third force $\overrightarrow {{F_3}} $

Assertion $A$ : If $A, B, C, D$ are four points on a semi-circular arc with centre at $'O'$ such that $|\overrightarrow{{AB}}|=|\overrightarrow{{BC}}|=|\overrightarrow{{CD}}|$, then $\overrightarrow{{AB}}+\overrightarrow{{AC}}+\overrightarrow{{AD}}=4 \overrightarrow{{AO}}+\overrightarrow{{OB}}+\overrightarrow{{OC}}$

Reason $R$ : Polygon law of vector addition yields $\overrightarrow{A B}+\overrightarrow{B C}+\overrightarrow{C D}+\overrightarrow{A D}=2 \overrightarrow{A O}$

In the light of the above statements, choose the most appropriate answer from the options given below

  • [JEE MAIN 2021]

The resultant force of $5 \,N$ and $10 \,N$ can not be ........ $N$

Let $\overrightarrow C = \overrightarrow A  + \overrightarrow B$

$(A)$ It is possible to have $| \overrightarrow C | < | \overrightarrow A |$ and $ | \overrightarrow C | < | \overrightarrow B|$

$(B)$ $|\overrightarrow C |$  is always greater than $|\overrightarrow A |$

$(C)$ $|\overrightarrow C |$ may be equal to $|\overrightarrow A | + |\overrightarrow B|$

$(D)$ $|\overrightarrow C |$ is never equal to $|\overrightarrow A | + |\overrightarrow B|$

Which of the above is correct

A car moves towards north at a speed of $54 \,km / h$ for $1 \,h$. Then it moves eastward with same speed for same duration. The average speed and velocity of car for complete journey is ..........