A student determined Young's Modulus of elasticity using the formula $Y=\frac{M g L^{3}}{4 b d^{3} \delta} .$ The value of $g$ is taken to be $9.8 \,{m} / {s}^{2}$, without any significant error, his observation are as following.

Physical Quantity	Least count of the Equipment used for measurement	Observed value
Mass $({M})$	$1\; {g}$	$2\; {kg}$
Length of bar $(L)$	$1\; {mm}$	$1 \;{m}$
Breadth of bar $(b)$	$0.1\; {mm}$	$4\; {cm}$
Thickness of bar $(d)$	$0.01\; {mm}$	$0.4 \;{cm}$
Depression $(\delta)$	$0.01\; {mm}$	$5 \;{mm}$

Then the fractional error in the measurement of ${Y}$ is

According to Joule's law of heating, heat produced $H = {I^2}\,Rt$, where I is current, $R$ is resistance and $t$ is time. If the errors in the measurement of $I, R$ and t are $3\%, 4\% $ and $6\% $ respectively then error in the measurement of $H$ is

The following observations were taken for determining surface tension $T$ of water by capillary method:

diameter of capillary, $D= 1.25 \times 10^{-2}\; m$

rise of water, $h=1.45 \times 10^{-2}\; m $ 

Using $g= 9.80 \;m/s^2$ and the simplified relation $T = \frac{{rhg}}{2}\times 10^3 N/m$ , the possible error in surface tension is ........... $\%$

A public park, in the form of a square, has an area of $(100 \pm 0.2)\; m ^2$. The side of park is ............ $m$

The relative error in the measurement of the side of a cube is $0.027$. The relative error in the measurement of its volume is .......... 

A metal wire has mass $(0.4 \pm 0.002)\,g$, radius $(0.3 \pm 0.001)\,mm$ and length $(5 \pm 0.02) \,cm$. The maximum possible percentage error in the measurement of density will nearly be $.......\%$