Two identical bodies, projected with the same speed at two different angles cover the same horizontal range $R$. If the time of flight of these bodies are 5 s and 10 s , respectively, then the value of $R$ is

$\_\_\_\_$ m.  (Take $g=10 \mathrm{~m} / \mathrm{s}^2$ )

A solid cylinder having radius $R$ and length $L$ is slipping on a rough horizontal plane. At time $t=0$ the cylinder has a translational velocity $v_{\mathrm{o}}=49 \mathrm{~m} / \mathrm{s}$, perpendicular to its axis and a rotational velocity $v_{\mathrm{o}} / 4 R$ about the centre. The time taken by the cylinder to start rolling is $\_\_\_\_$ seconds. (coefficient of kinetic friction $\mu_K=0.25$ and $g=9.8 \mathrm{~m} / \mathrm{s}^2$ )

A liquid of density $600 \mathrm{~kg} / \mathrm{m}^3$ flowing steadily in a tube of varying cross-section. The cross-section at a point $A$ is $1.0 \mathrm{~cm}^2$ and that at $B$ is $20 \mathrm{~mm}^2$. Both the points $A$ and $B$ are in same horizontal plane, the speed of the liquid at $A$ is $10 \mathrm{~cm} / \mathrm{s}$. The difference in pressures at $A$ and $B$ points is $\_\_\_\_$ Pa.

A spherical liquid drop of radius $R$ acquires the terminal velocity $v_1$ when falls through a gas of viscosity $\eta$. Now the drop is broken into 64 identical droplets and each droplet acquires terminal velocity $v_2$ falling through the same gas. The ratio of terminal velocities $v_1 / v_2$ is $\_\_\_\_$ .