The mechanical equivalent of heat $J$ is

Identify the pair whose dimensions are equal.

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 $\%$)

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

List-$I$	List-$II$
$(A)$ Mass density	$(I)$ $[ML^2T^{-3}]$
$(B)$ Impulse	$(II)$ $[MLT^{-1}]$
$(C)$ Power	$(III)$ $[ML^2T^0]$
$(D)$ Moment of inertia	$(IV)$ $[ML^{-3}T^0]$

Choose the correct answer from the options given below:

Express:
$(a)$ The energy required to break one bond in $DNA$ in $eV$.
$(b)$ The kinetic energy of an air molecule $(10^{-21} \; J)$ in $eV$.
$(c)$ The daily intake of a human adult in kilocalories.

Match List-$I$ with List-$II$ and select the correct answer.

List-$I$	List-$II$
$A$. Spring constant	$1$. $M^1L^2T^{-2}$
$B$. Pascal	$2$. $M^0L^0T^{-1}$
$C$. Hertz	$3$. $M^1L^0T^{-2}$
$D$. Joule	$4$. $M^1L^{-1}T^{-2}$