The length and width of a rectangular room are measured to be $3.95 \pm 0.05 \,m$ and $3.05 \pm 0.05 \,m$, respectively. The area of the floor is .................... $m^2$

Two clocks are being tested against a standard clock located in a national laboratory. At $12: 00: 00$ noon by the standard clock, the readings of the two clocks are 

$\begin{array}{ccc} & \text {Clock} 1 & \text {Clock} 2 \\ \text { Monday } & 12: 00: 05 & 10: 15: 06 \\ \text { Tuesday } & 12: 01: 15 & 10: 14: 59 \\ \text { Wednesday } & 11: 59: 08 & 10: 15: 18 \\ \text { Thursday } & 12: 01: 50 & 10: 15: 07 \\ \text { Friday } & 11: 59: 15 & 10: 14: 53 \\ \text { Saturday } & 12: 01: 30 & 10: 15: 24 \\ \text { Sunday } & 12: 01: 19 & 10: 15: 11\end{array}$

If you are doing an experiment that requires precision time interval measurements, which of the two clocks will you prefer?

Error in the measurement of radius of a sphere is $0.2\%$. The error in the calculated value of its volume is  ......... $\%$

The density of a material in the shape of a cube is determined by measuring three sides of the cube and its mass. If the relative errors in measuring the mass and length are respectively $1.5\%$ and $1\%$, the maximum error in determining the density is   ........ $\%$

Error in volume of a sphere is $6\%$. Error in its radius will be .......... $\%$

A person measures the depth of a well by measuring the time interval between dropping a stone and receiving the sound of impact with the bottom of the well. The error in his measurement of time is $\delta \mathrm{T}=0.01$ seconds and he measures the depth of the well to be $\mathrm{L}=20$ meters. Take the acceleration due to gravity $\mathrm{g}=10 \mathrm{~ms}^{-2}$ and the velocity of sound is $300 \mathrm{~ms}^{-1}$. Then the fractional error in the measurement, $\delta \mathrm{L} / \mathrm{L}$, is closest to