A student measured the diameter of a small steel ball using a screw gauge of least count $0.001$ cm. The main scale reading is $5$ mm and zero of circular scale division coincides with $25$ divisions above the reference level. If screw gauge has a zero error of $-0.004$ cm, the correct diameter of the ball is

In an experiment, the percentage of error occurred in the measurement of physical quantities A, B, C and D are $1\%, 2\%, 3\%$ and $4\%$ respectively. Then the maximum percentage of error in the measurement X, where $X = \frac{A^2 B^{\frac{1}{2}}}{C^{\frac{1}{3}} D^3},$ will be:

Taking into account the significant figures, what is the value of $9.99$ m $- 0.0099$ m$?$

A screw gauge has a least count of $0.01$ mm and there are $50$ divisions on its circular scale. The pitch of the screw gauge is:

If $E$ and $G$ respectively denote energy and gravitational constant, then $\frac{E}{G}$ has the dimensions of:

If force $[F],$ acceleration $[A]$ and time $[T]$ are chosen as the fundamental physical quantities, find the dimensions of energy.

Plane angle and solid angle have:

The area of a rectangular field (in $m^2$) of length $55.3$ m and breadth $25$ m after rounding off the value for correct significant digits is:

Match List - I with List - II regarding gravitational terms:

A metal wire has mass $(0.4 \pm 0.002)$ g, radius $(0.3 \pm 0.001)$ mm and length $(5 \pm 0.02)$ cm. The maximum possible percentage error in the measurement of density will nearly be:

The errors in the measurement which arise due to unpredictable fluctuations in temperature and voltage supply are:

In a vernier calipers, (N + 1) divisions of vernier scale coincide with N divisions of main scale. If 1 MSD represents 0.1 mm, the vernier constant (in cm) is:

A force defined by $F = \alpha t^2 + \beta t$ acts on a particle at a given time $t.$ The factor which is dimensionless, if $\alpha$ and $\beta$ are constants, is: