When a material particle of rest mass $m$ attains speed $c$ i.e. velocity of light, its mass becomes infinite.

A body of mass $5 \mathrm{kg}$ initially at rest explodes into $3$ fragments with mass ratio $3 : 1 : 1.$Two of fragments each of mass $\text{'}\mathrm{m}\text{'}$are found to move with a speed $60 \mathrm{m}/\mathrm{s}$ in mutually perpendicular directions. The magnitude of velocity of third fragment is :

A Space-ship in space will have :

(i) Clocks running slower than a stationary clock by a factor $\sqrt{1-\frac{{\mathrm{v}}^2}{{\mathrm{c}}^2}}$

(ii) Its length shrunk in the direction of the relative motion by factor of $\sqrt{1-\frac{{\mathrm{v}}^2}{{\mathrm{c}}^2}}$

(iii) Its mass is increased by a factor $\frac{1}{\sqrt{1-\frac{{\mathrm{v}}^2}{{\mathrm{c}}^2}}}$

Represent the union of two sets by Venn diagram for each of the following.

$X=\{x | x$ is a prime number between $80$ and $100\}$

$Y=\{y | y$ is an odd number between $90$ and $100\}$