The quantities which have the same dimensions as those of solid angle are:

Match the entries in List-$I$ with those in List-$II$.

$A$. Unified interaction reducing the number of fundamental forces from four to three	$(i)$ Strong interaction
$B$. Force between two molecules separated by a distance near about the sum of the molecular radii	$(ii)$ Gravitational force
$C$. Nuclear binding force	$(iii)$ Electroweak interaction
$D$. Bodies of astronomical proportions	$(iv)$ Electromagnetic interaction

Give an example of:
$(a)$ a physical quantity which has a unit but no dimensions
$(b)$ a physical quantity which has neither unit nor dimensions
$(c)$ a constant which has a unit
$(d)$ a constant which has no unit

Which of the following pairs of physical quantities does not have the same dimensional formula?

The dimensions of pressure are equal to

The coefficients of thermal expansion of steel and a metal $X$ are respectively $12 \times 10^{-6} /^{\circ}C$ and $2 \times 10^{-6} /^{\circ}C$. At $40^{\circ}C$,the side of a cube of metal $X$ was measured using a steel vernier callipers. The reading was $100 \, mm$. Assuming that the calibration of the vernier was done at $0^{\circ}C$,then the actual length of the side of the cube at $0^{\circ}C$ will be: