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

If error in measuring diameter of a circle is $4\%$, the error in radius of the circle would be

A body travels uniformly a distance of $ (13.8 \pm 0.2)\,m$ in a time $(4.0 \pm 0.3)\, s$. The percentage error in velocity is  ......... $\%$

While measuring the acceleration due to gravity by a simple pendulum, a student makes a positive error of $1\%$ in the length of the pendulum and a negative error of $3\%$ in the value of time period. His percentage error in the measurement of $g$ by the relation $g = 4{\pi ^2}\left( {l/{T^2}} \right)$ will be  ........ $\%$

Write type of error in measurement of physical quantity and explain.

The mean time period of second's pendulum is $2.00s$ and mean absolute error in the time period is $0.05s$. To express maximum estimate of error, the time period should be written as