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(D) The formula for Young's Modulus is $Y = \frac{FL}{A\ell} = \frac{mgL}{\pi R^2 \ell}$.The fractional error is given by $\frac{\Delta Y}{Y} = \frac{

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$1.4$

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(D) The formula for Young's Modulus is $Y = \frac{FL}{A\ell} = \frac{mgL}{\pi R^2 \ell}$.The fractional error is given by $\frac{\Delta Y}{Y} = \frac{\Delta m}{m} + \frac{\Delta L}{L} + 2\frac{\Delta R}{R} + \frac{\Delta \ell}{\ell}$.Given values:$m = 1 \, kg = 1000 \, g$,$\Delta m = 1 \, g$$L = 1 \, m = 1000 \, mm$,$\Delta L = 1 \, mm$$R = 0.2 \, cm$,$\Delta R = 0.001 \, cm$$\ell = 0.5 \, cm$,$\Delta \ell = 0.001 \, cm$Substituting these into the error formula:$\frac{\Delta Y}{Y} 	imes 100 = \left( \frac{1}{1000} + \frac{1}{1000} + 2 	imes \frac{0.001}{0.2} + \frac{0.001}{0.5} ight) 	imes 100$$= \left( 0.001 + 0.001 + 0.01 + 0.002 ight) 	imes 100$$= (0.001 + 0.001 + 0.01 + 0.002) 	imes 100 = 0.014 	imes 100 = 1.4 \%$.

System	Type of Elasticity
$(i)$ Suspension fibre of galvanometer	$(a)$ Linear
$(ii)$ Bending of beam	$(b)$ Shear
$(iii)$ Cutting piece of paper	$(c)$ Bulk
$(iv)$ Mechanical waves in fluid	$(d)$ Shear

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