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Question

(C) The formula for Young's modulus is $Y = \frac{F \cdot L}{A \cdot \Delta L}$.The dimensional formula for Young's modulus is $[Y] = [M L^{-1} T^{-2}

Vedclass · Accepted Answer

$0.1$

Vedclass · Answer

(C) The formula for Young's modulus is $Y = \frac{F \cdot L}{A \cdot \Delta L}$.The dimensional formula for Young's modulus is $[Y] = [M L^{-1} T^{-2}]$.In the $CGS$ system,the unit is $	ext{dyne/cm}^2$,and in the $MKS$ $(SI)$ system,the unit is $	ext{N/m}^2$.$1 	ext{ N/m}^2 = 1 \frac{	ext{kg} \cdot 	ext{m/s}^2}{	ext{m}^2} = 1 	ext{ kg} \cdot 	ext{m}^{-1} \cdot 	ext{s}^{-2}$.$1 	ext{ dyne/cm}^2 = 1 \frac{	ext{g} \cdot 	ext{cm/s}^2}{	ext{cm}^2} = 1 	ext{ g} \cdot 	ext{cm}^{-1} \cdot 	ext{s}^{-2}$.Converting $1 	ext{ dyne/cm}^2$ to $MKS$:$1 	ext{ g} = 10^{-3} 	ext{ kg}$$1 	ext{ cm}^{-1} = (10^{-2} 	ext{ m})^{-1} = 10^2 	ext{ m}^{-1}$.Therefore,$1 	ext{ dyne/cm}^2 = 10^{-3} 	ext{ kg} \cdot 10^2 	ext{ m}^{-1} \cdot 	ext{s}^{-2} = 10^{-1} 	ext{ N/m}^2 = 0.1 	ext{ N/m}^2$.Thus,the conversion factor from $CGS$ to $MKS$ is $0.1$.

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	$(IV)$ $ML^{-1}T^{-2}$

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 $(\phi)$	$(IV)$ $[M L^2 T^{-2}]$

List $I$	List $II$
$A$. Torque	$I$. $[M^1 L^1 T^{-2} A^{-2}]$
$B$. Magnetic field	$II$. $[L^2 A^1]$
$C$. Magnetic moment	$III$. $[M^1 T^{-2} A^{-1}]$
$D$. Permeability of free space	$IV$. $[M^1 L^2 T^{-2}]$

To determine Young's modulus of a wire,the formula is $Y = \frac{F}{A} \cdot \frac{L}{\Delta L}$,where $F/A$ is the stress and $L/\Delta L$ is the reciprocal of strain. The conversion factor to change $Y$ from $CGS$ to $MKS$ system is:

Similar Questions

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:

Identify the incorrect statement.

Which of the following pairs does not have the same dimensions?

Match List $I$ with List $II$:

List $I$ List $II$

$A$. Torque $I$. $[M^1 L^1 T^{-2} A^{-2}]$

$B$. Magnetic field $II$. $[L^2 A^1]$

$C$. Magnetic moment $III$. $[M^1 T^{-2} A^{-1}]$

$D$. Permeability of free space $IV$. $[M^1 L^2 T^{-2}]$

Choose the correct answer from the options given below:

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