Match List-$I$ with List-$II$:
List-$I$List-$II$
$(A)$ Torque$(I)$ $ML^{-2}T^{-2}$
$(B)$ Stress$(II)$ $ML^2T^{-2}$
$(C)$ Pressure gradient$(III)$ $ML^{-1}T^{-1}$
$(D)$ Coefficient of viscosity$(IV)$ $ML^{-1}T^{-2}$

Choose the correct answer from the options given below:

  • A
    $(A)-(III), (B)-(IV), (C)-(I), (D)-(II)$
  • B
    $(A)-(IV), (B)-(II), (C)-(III), (D)-(I)$
  • C
    $(A)-(II), (B)-(IV), (C)-(I), (D)-(III)$
  • D
    $(A)-(II), (B)-(I), (C)-(IV), (D)-(III)$

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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 $\%$)

The pair of physical quantities not having the same dimensions is:

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:

Fill in the blanks:
$(a)$ The volume of a cube of side $1\; cm$ is equal to $\ldots \ldots\, m ^{3}$
$(b)$ The surface area of a solid cylinder of radius $2.0 \;cm$ and height $10.0\; cm$ is equal to $\ldots(mm)^{2}$
$(c)$ $A$ vehicle moving with a speed of $18\; km\, h ^{-1}$ covers $\ldots ..m$ in $1\; s$
$(d)$ The relative density of lead is $11.3$. Its density is $\ldots ..\, g\, cm ^{-3}$ or $\ldots . .\, kg\, m ^{-3}$.

$A$ steel tape gives correct measurement at $20^{\circ}C$. $A$ piece of wood is being measured with the steel tape at $0^{\circ}C$. The reading is $25 \, cm$ on the tape. The real length of the given piece of wood must be:

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