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In the expression for time period $T$ of simple pendulum $T=2 \pi \sqrt{\frac{l}{g}}$, if the percentage error in time period $T$ and length $l$ are $2 \%$ and $2 \%$ respectively then percentage error in acceleration due to gravity $g$ is equal to ......... $\%$
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 student measures the thickness of a human hair by looking at it through a microscope of magnification $100$. He makes $20$ observations and finds that the average width of the hair in the field of view of the microscope is $3.5 \;mm$. What is the estimate on the thickness(in $mm$) of hair ?
The vernier constant of Vernier callipers is $0.1 \,mm$ and it has zero error of $(-0.05) \,cm$. While measuring diameter of a sphere, the main scale reading is $1.7 \,cm$ and coinciding vernier division is $5$. The corrected diameter will be ........... $\times 10^{-2} \,cm$
In an experiment with Vernier callipers of least count $0.1\,mm$, when two jaws are joined together the zero of Vernier scale lies right to the zero of the main scale and $6^{\text {th }}$ division of Vernier scale coincides with the main scale division. While measuring the diameter of a spherical bob, the zero of vernier scale lies in between $3.2\,cm$ and $3.3\,cm$ marks, and $4^{\text {th }}$ division of vernier scale coincides with the main scale division. The diameter of bob is measured as $.......\,cm$