The ratio $\left(\frac{E}{W}\right)$ of relative strength of electromagnetic force $(E)$ to weak nuclear force $(W)$ is,

Estimate the average mass density of a sodium atom assuming its size to be about $2.5 \; \mathring{A}$. (Use the known values of Avogadro's number and the atomic mass of sodium). Compare it with the mass density of sodium in its crystalline phase: $970 \; kg \; m^{-3}$. Are the two densities of the same order of magnitude? If so,why?

Match List-$I$ with List-$II$.

List-$I$	List-$II$
$(A)$ Torque	$(I)$ $Nms^{-1}$
$(B)$ Stress	$(II)$ $Jkg^{-1}$
$(C)$ Latent Heat	$(III)$ $Nm$
$(D)$ Power	$(IV)$ $Nm^{-2}$

Choose the correct answer from the options below.

State,for each of the following physical quantities,if it is a scalar or a vector: volume,mass,speed,acceleration,density,number of moles,velocity,angular frequency,displacement,angular velocity.

The pair having the same dimensions is

The maximum percentage errors in the measurement of mass $(M)$,radius $(R)$,and angular velocity $(\omega)$ of a ring are $2 \%$,$1 \%$,and $1 \%$ respectively. Find the maximum percentage error in the measurement of its rotational kinetic energy $(K = \frac{1}{2} I \omega^{2})$. (in $\%$)