The time taken by a block of mass $m$ to slide down from the highest point to the lowest point on a rough inclined plane is $50 \%$ more compared to the time taken by the same block on identical inclined smooth plane. Both inclined planes are at $45^{\circ}$ with the horizontal. The coefficient of kinetic friction between the rough inclined surface and block is $\_\_\_\_$

Two nuclei of mass number 3 combine with another nucleus of mass number 4 to yield a nucleus of mass number 10. If the binding energy per nucleon for the mass numbers 3,4 and 10 are $5.6 \mathrm{MeV}, 7.4 \mathrm{MeV}$ and 6.1 MeV , respectively, then in the process, $\Delta \mathrm{Mc}^2=$ $\_\_\_\_$ MeV .

A solid sphere of mass $M$ and radius $R$ is divided into two unequal parts. The smaller part having mass $M / 8$ is converted into a sphere of radius $r$ and the larger part is converted into a circular disc of thickness $t$ and radius $2 R$. If $I_1$ is moment of inertia of a sphere having radius $r$ about an axis through its centre and $I_2$ is the moment of inertia of a disc about its diameter, the ratio of their moment of inertia $I_2 / I_1=$ $\_\_\_\_$

The two projectiles are projected with the same initial velocities at the $15^{\circ}$ and $30^{\circ}$ with respect to the horizontal. The ratio of their ranges is $1: x$. The value of $x$ is