The physical quantities that have the same dimensions are:

The diameter of a wire measured by a screw gauge of least count $0.001 \text{ cm}$ is $0.08 \text{ cm}$. The length measured by a scale of least count $0.1 \text{ cm}$ is $150 \text{ cm}$. When a weight of $100 \text{ N}$ is applied to the wire, the extension in length is $0.5 \text{ cm}$, measured by a micrometer of least count $0.001 \text{ cm}$. The error in the measured Young's modulus is $\alpha \times 10^9 \text{ N/m}^2$. The value of $\alpha$ is . . . . . . . (Ignore the contribution of the load to Young's modulus error calculation)

Match the following (Take the relative strength of the strongest fundamental forces in nature as $1$):

$I$ (Fundamental forces in nature)	$II$ (Relative strength)
$(A)$ Strong nuclear force	$(e)$ $10^{-2}$
$(B)$ Weak nuclear force	$(f)$ $1$
$(C)$ Electromagnetic force	$(g)$ $10^{10}$
$(D)$ Gravitational force	$(h)$ $10^{-13}$
	$(i)$ $10^{-39}$

The correct match is:

$0.1 \, Pa = \dots \, Nm^{-2} = \dots \, \text{dyne} \, cm^{-2}$.

If $\epsilon_0$, $E$, and $t$ represent the free space permittivity, electric field, and time respectively, then the unit of $\frac{\epsilon_0 E}{t}$ will be:

In a new system,the unit of mass is $10 \ kg$,the unit of length is $5 \ m$,and the unit of time is $10 \ s$. Then,in this new system,$20 \ g/cm^3$ is equal to: