$A$ thin rod of length $L$ is bent to form a semicircle. The mass of the rod is $M$. What will be the gravitational potential at the centre of the circle?

If $x=p+q$,$y=p \omega+q \omega^2$,and $z=p \omega^2+q \omega$,where $\omega$ is a complex cube root of unity,then $xyz$ is equal to:

If $u=\sin ^{-1}\left(\frac{x^4+y^4}{x+y}\right)$,then $x \frac{\partial u}{\partial x}+y \frac{\partial u}{\partial y}$ is equal to

Who discovered $TMV$ (Tobacco Mosaic Virus)?

$A$ small mass $m$ is attached to a massless string whose other end is fixed at $P$ as shown in the figure. The mass is undergoing circular motion in the $x-y$ plane with center $O$ and constant angular speed $\omega$. If the angular momentum of the system,calculated about $O$ and $P$ is denoted by $\vec L_o$ and $\vec L_p$ respectively,then:

Which of the following is an incorrect pair?