$A$ ray of light along $x+\sqrt{3}y=\sqrt{3}$ gets reflected upon reaching the $x$-axis. The equation of the reflected ray is:

The quadratic equation whose roots are $\sin ^2 18^{\circ}$ and $\cos ^2 36^{\circ}$ is :

$A$ load of $1 ~kg$ weight is attached to one end of a steel wire of area of cross-section $3 ~mm^2$ and Young's modulus $10^{11} ~N/m^2$. The other end is suspended vertically from a hook on a wall,then the load is pulled horizontally and released. When the load passes through its lowest position,the fractional change in length is $(g = 10 ~m/s^2)$.

The potential energy for a force field $\vec{F}$ is given by $U(x, y) = \cos(x + y)$. The force acting on a particle at the position given by coordinates $(0, \pi/4)$ is:

The adjacent graph shows the extension $(\Delta l)$ of a wire of length $1 \ m$ suspended from the top of a roof at one end with a load $W$ connected to the other end. If the cross-sectional area of the wire is $10^{-6} \ m^2$,calculate the Young's modulus of the material of the wire.

Two spherical conductors $A$ and $B$ of radii $1 \ mm$ and $2 \ mm$ are separated by a distance of $5 \ cm$ and are uniformly charged. If the spheres are connected by a conducting wire,then in the equilibrium condition,the ratio of the magnitude of the electric fields at the surfaces of spheres $A$ and $B$ is-