A binary star consists of two stars $\mathrm{A}$ (mass $2.2 \mathrm{M}_5$ ) and $\mathrm{B}$ (mass $11 \mathrm{M}_5$ ), where $\mathrm{M}_5$ is the mass of the sun. They are separated by distance $\mathrm{d}$ and are rotating about their centre of mass, which is stationary. The ratio of the total angular momentum of the binary star $\mathrm{A}$ to the angular momentum of star $\mathrm{B}$ about the centre of mass is

A flywheel can rotate in order to store kinetic energy. The flywheel is a uniform disk made of a material with a density $\rho $ and tensile strength $\sigma $ (measured in Pascals), a radius $r$ , and a thickness $h$ . The flywheel is rotating at the maximum possible angular velocity so that it does not break. Which of the following expression correctly gives the maximum kinetic energy per kilogram that can be stored in the flywheel ? Assume that $\alpha $ is a dimensionless constant

A particle is moving in a circular path of radius $a,$ with a constant velocity $v$ as shown in the figure.The centre of circle is marked by $'C'$. The angular momentum from the origin $O$ can be written as

$A$ particle of mass $m$ is rotating in a plane is $a$ circular path of radius $r$, its angular momentum is $L$. The centripital force acting on the particle is :

A disc of mass $M$ and radius $R$ moves in the $x-y$ plane as shown in the figure. The angular momentum of the disc at the instant shown is