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The pitch and the number of divisions, on the circular scale, for a given screw gauge are $0.5\,mm$ and $100$ respectively. When the screw gauge is fully tightened without any object, the zero of its circular scale lies $3$ divisions below the mean line. The readings of the main scale and the circular scale for a thin sheet, are $5.5\,mm$ and $48$ respectively, the thickness of this sheet is
A small steel ball of radius $r$ is allowed to fall under gravity through a column of a viscous liquid of coefficient of viscosity $\eta $. After some time the velocity of the ball attains a constant value known as terminal velocity ${v_T}$. The terminal velocity depends on $(i)$ the mass of the ball $m$, $(ii)$ $\eta $, $(iii)$ $r$ and $(iv)$ acceleration due to gravity $g$. Which of the following relations is dimensionally correct
The resistance $R =\frac{ V }{ I },$ where $V =(50 \pm 2) \;V$ and $I=(20 \pm 0.2)\;A.$ The percentage error in $R$ is $x\%$. The value of $x$ to the nearest integer is .........
The period of a body under SHM i.e. presented by $T = {P^a}{D^b}{S^c}$; where $P$ is pressure, $D$ is density and $S$ is surface tension. The value of $a,\,b$ and $c$ are
If the random error in the arithmetic mean of $50$ observations is $\alpha$, then the random error in the arithmetic mean of $150$ observations would be