Mock Test 1 — Units, Dimensions and Measurements

The dimensional formula for coefficient of viscosity is:

If velocity, time, and force are taken as fundamental quantities, the dimensions of mass are:

A physical quantity is given by $X = M^a L^b T^c$. Percentage errors in $M, L, T$ are $\alpha\%, \beta\%, \gamma\%$ respectively. The maximum percentage error in $X$ is:

The value of $1$ joule expressed in a system where unit of mass = $\alpha$ kg, length = $\beta$ m, time = $\gamma$ s equals:

The dimensions of $\frac{1}{\sqrt{\mu_0 \varepsilon_0}}$ are:

The percentage errors in measurement of mass and speed are $2\%$ and $3\%$ respectively. The maximum percentage error in kinetic energy is:

If $E, M, J,$ and $G$ denote energy, mass, angular momentum, and gravitational constant respectively, the dimensions of $\dfrac{EJ^2}{M^5 G^2}$ are:

The least count of a screw gauge of pitch $0.5$ mm with $50$ circular divisions is:

The radius of a sphere is measured to be $(2.1 \pm 0.1)$ cm. The percentage error in volume is:

The number of significant figures in $0.003050$ is:

A quantity $X = \dfrac{a^2 b^3}{c^4}$. If errors are $1\%$ in $a$, $2\%$ in $b$, and $1\%$ in $c$, find the maximum percentage error in $X$ (as an integer).

The pitch of a screw gauge is $1$ mm and there are $100$ divisions on its circular scale. While measuring the diameter of a wire, MSR is $0$, and CSR is $52$. The diameter of the wire in $\mu$m is:

The percentage error in the period of a pendulum is $1\%$ and in length is $2\%$. The percentage error in $g$ (rounded to an integer) is:

Assertion (A): The equation $s = ut + \frac{1}{2}at^2$ is dimensionally correct. Reason (R): A dimensionally correct equation must be physically correct.

Assertion (A): A screw gauge having pitch $1$ mm with $100$ divisions on the circular scale is more accurate than a vernier caliper with $10$ VSD = $9$ MSD (1 MSD = 1 mm). Reason (R): A smaller least count implies higher precision.