Units & measurements practice · Medium

How many wavelengths of $K{r^{86}}\mathrm{\;}$ are there in one metre

A student writes four different expressions for the displacement $y$ in a periodic motion as a function of time $t, a$ as amplitude, $T$ as time period. Which of the following can be correct?

Which is wrong dimension

Assertion: Surface tension and surface energy have the same dimensions.

Reason: Because both have the same S.I. unit

In the context of accuracy of measurement and significant figures in expressing results of experiment, which of the following is/are correct
(1) Out of the two measurements 50.14 cm and 0.00025 ampere, the first one has greater accuracy
(2) If one travels 478 km by rail and 397 m by road, the total distance travelled is 478 km

Volt/metre is the unit of

Given that ${y}={A} \sin ({aEt}-{bVx})$ where ${y}$ displacement, ${E}$ energy, ${V}$ is velocity, ${t}$ and ${x}$ are time and distance respectively then, the dimension of ${a / b}$ is:

In an expression $\mathrm{a} \times 10^{\mathrm{b}}$ :

In an experiment four quantities $a, b, c$ and $d$ are measured with percentage error $2 \%, 3 \%, 4 \%$ and $1 \%$ respectively. Quantity $P$ is calculated as follows; $P=\frac{a^3 b^2}{c d}$. Percentage error in $P$ is;

Consider the following statements and select the correct
statement(s).
I. 1 calorie = 4.18 joule
II. $1\stackrel{o}{A}=10^{-10} \mathrm{~m}$
III. $1 \mathrm{MeV}=1.6 \times 10^{-13}$ Joule
IV. 1 newton $=10^{-5}$ dyne

$N m^2 /kg^2$ is a unit of

The dimension of $\mathrm{E} / \mathrm{H}$ is that of

Find the number of significant digits in the value $10.05.$

Which of the following is not one of the seven fundamental SI units?

If the velocity $(V)$, acceleration $(A)$, and force $(F)$ are taken as fundamental quantities instead of mass $(M)$, length $(L)$, and time $(T)$, the dimensions of Young's modulus $(Y)$ would be

Statement-I: Linear momentum and moment of force have same dimensions.
Statement-II: Planck’s constant and angular momentum have same dimension.

The dimensions of farad are

The dimensions of $\mathrm{h} / \mathrm{e}(\mathrm{h}=$ Planck's constant and $\mathrm{e}=$ electronic charge) are same as that of:

In which of the following numerical values, all zeros are significant?

A physical quantity $P=\frac{\sqrt{a b c^2}}{d^3}$ is determined by measuring $a, b, c$, and $d$ separately with the percentage error of $2 \%, 3 \%, 2 \%$, and $1 \%$, respectively. Minimum amount of error is contributed by:

Assertion : In the equation momentum, $P = \frac{{mass}}{{area}}x,$ the dimensional formula of $x$ is $L{T^{ - 2}}.$
Reason : Quantities with different dimensions can be multiplied.

If $L, C$ and $R$ denote the inductance, capacitance and resistance respectively, the dimensional formula for $C^2 L R$ is

Assertion: $\mu \mathrm{N}$ is not the same as $\mathrm{nm}$.
Reason: $1 \mu \mathrm{N}=10^{-6} \mathrm{~N}$ and $1 \mathrm{~nm}=10^{-9} \mathrm{~m}$

The dimensions of $\frac{1}{{{ \in _0}}}\frac{{{e^2}}}{{hc}}$ are

In the formula $F=A . e^{\frac{h c}{x}}$, where $h$ is Planck's constant, and $c$ is speed of light. The dimensional formula for $x$ is

If C,R,L and I denote capacity, resistance, inductance and electric current respectively, the quantities having the same dimensions of time are $\left( 1 \right)\,CR,\,\,\left( 2 \right)\,\frac{L}{R}\,,\,\,\left( 3 \right)\,\sqrt {LC} \,\,\left( 4 \right)\,L{I^2}$

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 $\frac{{\Delta A}}{A} = \frac{{4\Delta r}}{r}$

The pitch of screw gauge is $1 \mathrm{~mm}$ and there are 100 divisions on circular scale. While measuring diameter of a wire, linear scale reads $1 \mathrm{~mm}$ and $39^{\text {th}}$ division of circular scale coincides with reference line. The zero error is $-0.05 \mathrm{~mm}$. The correct diameter of wire is

If Planck's constant $(h)$ and speed of light in vacuum $(c)$ are taken as two fundamental quantities, which one of the following can, in addition, be taken to express length, mass and time in terms of the three chosen fundamental quantities?

(i) Mass of electron $\left(m_e\right)$

(ii) Universal gravitational constant $(G)$

(iii) Charge of electron $(e)$

(iv) Mass of proton $\left(m_p\right)$

Inductance L can be dimensionally represented as