The quantities which have the same dimensions | vedclass

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(D) The solid angle is defined as $d\Omega = \frac{dA}{r^2}$. Since it is the ratio of area to the square of distance,its dimensions are $[M^0 L^0 T^0

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strain and angle

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(D) The solid angle is defined as $d\Omega = \frac{dA}{r^2}$. Since it is the ratio of area to the square of distance,its dimensions are $[M^0 L^0 T^0]$,making it a dimensionless quantity.Strain is defined as the ratio of change in length to original length,$	ext{Strain} = \frac{\Delta l}{l}$,which is also dimensionless $[M^0 L^0 T^0]$.An angle $	heta = \frac{l}{r}$ is the ratio of arc length to radius,which is also dimensionless $[M^0 L^0 T^0]$.Therefore,both strain and angle have the same dimensions as a solid angle.

Column-$I$	Column-$II$
$(a)$ Ratio of change in time period of a simple pendulum with temperature to its original time period	$(i) \, \alpha \Delta T$
$(b)$ Ratio of the value of a length to its scale reading	$(ii) \, T$
$(c)$ Reciprocal of coefficient of volume expansion for an ideal gas of constant pressure	$(iii) \, (1 + \alpha \Delta T)$
$(d) \, \frac{F}{YA} =$	$(iv) \, \frac{1}{2} \alpha \Delta T$

List-$I$	List-$II$
$A$. Young's Modulus $(Y)$	$I$. $[M L^{-1} T^{-1}]$
$B$. Co-efficient of Viscosity $(\eta)$	$II$. $[M L^2 T^{-1}]$
$C$. Planck's Constant $(h)$	$III$. $[M L^{-1} T^{-2}]$
$D$. Work Function $(\varphi)$	$IV$. $[M L^2 T^{-2}]$

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

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