A thin uniform rod of length $2$ m cross-sectional area 'A' and density 'd' is rotated about an axis passing through the centre and perpendicular to its length with angular velocity $\omega$. If the value of $\omega$ in terms of its rotational kinetic energy $E$ is $(\alpha E/Ad)^{1/2}$, then the value of $\alpha$ is

If earth has a mass nine times and radius twice to the planet P. Then $\dfrac{v_e}{3}\sqrt{x}$ ms$^{-1}$ will be the minimum velocity required by a rocket to pull out of gravitational force of P, where $v_e$ is escape velocity on earth. The value of $x$ is

Determine the ratio of surface energy of $1$ large drop to $1$ small drop, if $1000$ small drops combined to form $1$ large drop.

A spherical drop of liquid splits into $1000$ identical spherical drops. If $u_i$ is the surface energy of the original drop and $u_f$ is the total surface energy of the resulting drops, the (ignoring evaporation). $u_f / u_i = (10/x)$. Then value of $x$ is