When the gap is closed without placing any object in the screw gauge whose least count is $0.005\ mm$ , the $5^{th}$ division on its circular scale with the reference line on main scale, and when a small sphere is placed reading on main scale advances by $4$ divisions, whereas circular scale reading advances by five times to the corresponding reading when no object was placed. There are $200$ divisions on the circular scale. The radius of the sphere is  ………. $mm$

A set of defective observation of weights is used by a student to find the mass of an object using a physical balance. A large number of readings will reduce

The time period of a body undergoing simple harmonic motion is given by $T=p^{a} D^{b} S^{c}$, where $p$ is the pressure, $D$ is density and $S$ is surface tension. The values of $a, b$ and $c$ respectively are

The least count of a stop watch is $\frac{1}{5}$ second. The time of $20$ oscillations of a pendulum is measured to be $25$ seconds. The maximum percentage error in the measurement of time will be ………. $\%$

If $Q = \frac{{{X^n}}}{{{Y^m}}}$ and $\Delta X$ is absolute error in the measurement of $X, \Delta Y$ is absolute error in the measurement of $Y,$ then absolute error $\Delta Q$ in $Q$ is