The dimensions of ${e^2}/4\pi {\varepsilon _0}hc$, where $e,\,{\varepsilon _0},\,h$ and $c$ are electronic charge, electric permittivity, Planck’s constant and velocity of light in vacuum respectively
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In a simple pendulum experiment for determination of acceleration due to gravity $(g)$, time taken for $20$ oscillations is measured by using a watch of $1$ second least count. The mean value of time taken comes out to be $30s$. The length of pendulum is measured by using a meter scale of least count $1\ mm$ and the value obtained is $55.0\ cm$. The percentage error in the determination of $g$ is close to $ ........... \%$
In an experiment four quantities $a, b, c$ and $d$ are measured with percentage error $1\%, 2\%, 3\%$ and $4\%$ respectively. Quantity $w$ is calculated as follows $w\, = \,\frac{{{a^4}{b^3}}}{{{c^2}\sqrt D }}$ error in the measurement of $w$ is .......... $\%$
A student performs an experiment of measuring the thickness of a slab with a vernier calliper whose $50$ divisions of the vernier scale are equal to $49$ divisions of the main scale. He noted that zero of the vernier scale is between $7.00\; cm$ and $7.05 \;cm$ mark of the main scale and $23^rd$ division of the vernier scale exactly coincides with the main scale. The measured value of the thickness of the given slab using the calliper will be
A travelling microscope is used to determine the refractive index of a glass slab. If $40$ divisions are there in $1 \; cm$ on main scale and $50$ Vernier scale divisions are equal to $49$ main scale divisions, then least count of the travelling microscope is $\dots \; \times 10^{-6} \; m$