The radius of a sphere is measured to be $(7.50 \pm 0.85) \,cm .$ Suppose the percentage error in its volume is $x$. The value of $x$, to the nearest integer is .....$\%$

An optical bench has $1.5 m$ long scale having four equal divisions in each $cm$. While measuring the focal length of a convex lens, the lens is kept at $75 cm$ mark of the scale and the object pin is kept at $45 cm$ mark. The image of the object pin on the other side of the lens overlaps with image pin that is kept at $135 cm$ mark. In this experiment, the percentage error in the measurement of the focal length of the lens is. . . . .

The random error in the arithmetic mean of $100$ observations is $x$; then random error in the arithmetic mean of $400$ observations would be

The values of a number of quantities are used in a mathematical formula. The quantity that should be most precise and accurate in measurement is the one

The period of oscillation of a simple pendulum is $T=2 \pi \sqrt{L / g}$ Measured value of $L$ is $20.0 \;cm$ known to $1\; mm$ accuracy and time for $100$ oscillations of the pendulum is found to be $90 \;s$ using a wrist watch of $1\; s$ resolution. What is the accuracy in the determination of $g in \% ?$

Explain least count and least count error. Write a note on least count error.