Q 11-06-116JEE MainJEE Main 2023 (10 Apr, Shift 2)Medium
A force of $-P\hat k$ acts on the origin of the coordinate system. The torque about the point $(2,-3)$ is $P\left(a\hat i+b\hat j\right)$. The ratio of $\dfrac ab$ is $\dfrac x2$. The value of $x$ is ______.
Numerical value type. Enter your answer.
Answer: 3
Position of the point of application relative to $(2,-3)$: $\vec r=(0-2)\hat i+(0+3)\hat j=-2\hat i+3\hat j$.
$$\vec\tau=\vec r\times\vec F=(-2\hat i+3\hat j)\times(-P\hat k)=2P(\hat i\times\hat k)-3P(\hat j\times\hat k)=-3P\hat i-2P\hat j$$
$a=-3$, $b=-2$, $\dfrac ab=\dfrac32$, so $x=3$.
Solution by Sreeraj P, M.Sc Physics