$A$ student measures the distance traversed in free fall of a body,initially at rest,in a given time. He uses this data to estimate $g$,the acceleration due to gravity. If the maximum percentage errors in measurement of the distance and the time are $e_1$ and $e_2$ respectively,the percentage error in the estimation of $g$ is:

Write the types of errors in the measurement of a physical quantity and explain them.

$A$ physical quantity $X$ is related to four measurable quantities $a, b, c$ and $d$ as follows: $X = a^2b^3c^{\frac{5}{2}}d^{-2}$. The percentage errors in the measurement of $a, b, c$ and $d$ are $1\%$,$2\%$,$3\%$ and $4\%$ respectively. What is the percentage error in quantity $X$? If the value of $X$ calculated on the basis of the above relation is $2.763$,to what value should you round off the result?

The initial and final temperatures of water in a container are observed to be $16 \pm 0.6 \ ^\circ C$ and $56 \pm 0.3 \ ^\circ C$. What will be the rise in temperature of the water?

$A$ particle covers a distance of $(13.8 \pm 0.2) \ m$ in $(4 \pm 0.3) \ s$. Its velocity under error limits will be

The error in the measurement of length and mass is $3 \%$ and $4 \%$ respectively. The error in the measurement of density will be (in $\%$)