A torque meter is calibrated to reference standards of mass, length and time each with $5 \%$ accuracy. After calibration, the measured torque with this torque meter will have net accuracy of$............\%$

The period of oscillation of a simple pendulum is $T =2 \pi \sqrt{\frac{ L }{ g }} .$ Measured value of $ L $ is $1.0\, m$ from meter scale having a minimum division of $1 \,mm$ and time of one complete oscillation is $1.95\, s$ measured from stopwatch of $0.01 \,s$ resolution. The percentage error in the determination of $g$ will be ..... $\%.$

In an experiment of determine the Young's modulus of wire of a length exactly $1\; m$, the extension in the length of the wire is measured as $0.4\,mm$ with an uncertainty of $\pm 0.02\,mm$ when a load of $1\,kg$ is applied. The diameter of the wire is measured as $0.4\,mm$ with an uncertainty of $\pm 0.01\,mm$. The error in the measurement of Young's modulus $(\Delta Y)$ is found to be $x \times 10^{10}\,Nm ^{-2}$. The value of $x$ is

$\left[\right.$ Take $\left.g =10\,m / s ^{2}\right]$

If the error in the measurement of radius of a sphere is $2\%$ then the error in the determination of volume of the sphere will 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  ......... $\%$

The International Avogadro Coordination project created the world's most perfect sphere using Silicon in its crystalline form. The diameter of the sphere is $9.4 \,cm$ with an uncertainty of $0.2 \,nm$. The atoms in the crystals are packed in cubes of side $a$. The side is measured with a relative error of $2 \times 10^{-9}$, and each cube has $8$ atoms in it. Then, the relative error in the mass of the sphere is closest to (assume molar mass of Silicon and Avogadro's number to be known precisely)