d (d) Joule-sec is the unit of angular momentum where as other units are of energy.
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A screw gauge with a pitch of $0.5 \ mm$ and a circular scale with $50$ divisions is used to measure the thickness of a thin sheet of Aluminium. Before starting the measurement, it is found that wen the two jaws of the screw gauge are brought in contact, the $45^{th} $division coincides with the main scale line and the zero of the main scale is barely visible. What is the thickness of the sheet (in $mm$) if the main scale reading is $0.5\ mm$ and the $25^{th}$ division coincides with the main scale line
In the relation $P = \frac{\alpha }{\beta }{e^{ - \frac{{\alpha Z}}{{k\theta }}}}$ $P$ is pressure, $Z$ is the distance, $k$ is Boltzmann constant and $\theta$ is the temperature. The dimensional formula of $\beta$ will be
Young-Laplace law states that the excess pressure inside a soap bubble of radius $R$ is given by $\Delta P=4 \sigma / R$, where $\sigma$ is the coefficient of surface tension of the soap. The EOTVOS number $E_0$ is a dimensionless number that is used to describe the shape of bubbles rising through a surrounding fluid. It is a combination of $g$, the acceleration due to gravity $\rho$ the density of the surrounding fluid $\sigma$ and a characteristic length scale $L$ which could be the radius of the bubble. A possible expression for $E_0$ is
In a particular system the units of length, mass and time are chosen to be $10\;cm , 10 \;g$, and $0.1\;s$ respectively. The units of force in this system will be equal to?