Units & measurements practice · Mixed difficulty

The length, breadth and thickness of a metal block is given by $l = 90 cm$, b=8 cm, t=2.45 cm. The volume of the block is

Statement-I: The quantity $\frac{e^2}{\epsilon_0 c h}$ is dimensionless
Statement II: $\frac{1}{\sqrt{\mu_0 \epsilon_0 }}$ has the dimensions of velocity and is numerically equal of velocity of light.

The vernier scale of a callipers is divided into 20 divisions which coincide with 18 main scale divisions. Each main scale division is 0.2 mm. The least count of the instrument is

$\left[ {M{L^2}{T^{ - 3}}} \right]$ is the dimension of

If $X = A \times B$ and $\Delta X$ and ∆A and ∆B are maximum absolute errors in X, A and B respectively, then the maximum relative error in X is given by

A quantity $y$ is related to another quantity $\mathrm{x}$ by the equation $\mathrm{y}=\mathrm{kx}^{\mathrm{a}}$ where $\mathrm{k}$ and $\mathrm{a}$ are constant. If percentage error in the measurement of $x$ is $p$, then error in $y$ depends upon

Surface tension has the same dimensions as that of

If $x = \frac{{{A^2}{B^3}}}{{C\sqrt D }}$ and percentage errors in A, B, C & D are 1%, 2%, 3% and 4% respectively, the percentage error in $x$ is

If P represents radiations pressure, c represents speed of light and Q represents radiation energy striking a unit area per second, the non-zero integers x,y and z such that ${P^x}{Q^y}{c^z}$ is dimensionless, are

Assertion The error in the measurement of radius of the sphere is $0.3 \%$. The permissible error in its surface area is $0.6 \%$.

Reason The permissible error is calculated by the formula $\frac{\Delta A}{A}=4 \frac{\Delta r}{r}$

Read the following statements and Identify the correct statement/s. A: A choice of change of different units change the number of significant digits. B: To remove ambiguities in determining the number of significant figures, the best way is to report the measurement in scientific notation. C: Solid angle made by a hemisphere at its centre is $2\pi$ steradian.

The mass of the liquid flowing per second per unit area of cross-section of the tube is proportional to (pressure difference across the ends) $^n$ and (average velocity $^m$ of the liquid. Which one of the following relation is correct?

Which one has the dimensions different from the remaining three

The dimensional formula for Reynold's number is

If the length of rod A is $\left( {3.25\; \pm 0.01} \right)\;\mathrm{cm}$ and that of B is $\left( {4.19\; \pm 0.01} \right)\mathrm{\;cm},$, then the rod B is longer than rod A by

Out of the following which pair of quantities do not have same dimensions

In the relation $x = \cos \left( {\mathrm{\omega }t + kx} \right),$ the dimensions of ω are

A physical quantity $Q$ depends on other physical quantities $a, b$ and $c$ as $Q=\frac{a^4 b^3}{c^2}$
If maximum percentage error in measurement of $a$, $b$ and $c$ are $3 \%, 4 \%$ and $5 \%$ respectively, then find maximum percentage error in measurement of $Q$.

If force (F) , length (L) and time (T) are assumed to be fundamental units, then the dimensional formula of the mass will be

The position of a particle at time t is given by the relation $x\left( t \right) = \left( {\frac{{{v_0}}}{\alpha }} \right)\left( {1 - {c^{ - \alpha t}}} \right)$, where ${v_0}$ is a constant and $\alpha > 0$. The diemensions of ${v_0}$ and $\alpha$ are respectively

Select the pair whose dimensions are same

If $\varepsilon_0$ is the permittivity of free space and $E$ is the electric field, then $\varepsilon_0 E^2$ has the dimensions:

If the digit to be dropped is more than 5, then the preceding digit is _____.

When 57.986 is rounded off to 4 significant figures then it becomes

State the number of significant figures in the
following:
(i) 2.000 m (ii) 5100 kg (iii) 0.050 cm.

The dimensions of universal gas constant is

The displacement of an oscillating particle is given by $y=A \sin (B x+C t+D)$. The dimensional formula for $(A B C D)$ is

The unit of e.m.f. is

Which of the following quantities have the same dimensions?
a. Surface tension $\quad$ b. Spring constant $\quad$ c. Tension

Which physical quantities have same dimensions?