Units & measurements practice · Mixed difficulty

What is the SI unit of electron mobility?

A torque meter is calibrated to reference standards of mass, length and time each with $5 \%$ accuracy. After calibration, the measured torque with this torque meter will have net accuracy of

Dimensional formula for the plank’s constant is

The dimension of $\left(\mu_0 \varepsilon_0\right)^{-1 / 2}$ are

Which of the following represents a volt

The dimension of magnetic field in M, L, T and C (coulomb) is given as

The dimensions of calorie are

The dimensions of stress are equal to

What is the dimensional formula of $m{c^2}$, where the letters have their usual meanings?

Which of the following pair of quantities do not have the same dimensions :

If velocity v, acceleration A and force F are chosen a fundamental quantities, then the dimensional formula of angular momentum in terms of v,A and F would be

The unit of potential energy is

The thrust developed by a rocket-motor is given by $F = mv + A\left( {{p_1} - {p_2}} \right)$, where m is the mass of the gas ejected per unit time, $v$ is velocity of the gas, A is area of cross-section of the nozzle, ${p_1}.{p_2}$ are the pressures of the exhaust gas and surrounding atmosphere. The formula is dimensionally

Assertion : The number of significant figures depends on the least count of measuring instrument.

Reason : Significant figures define the accuracy of measuring instrument.

Unit of Stefan's constant is

Which of the following is not represented in correct unit

Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R).

Assertion (A) : In Vernier calliper if positive zero error exists, then while taking measurements, the reading taken will be more than the actual reading.

Reason (R) : The zero error in Vernier Calliper might have happened due to manufacturing defect or due to rough handling.
In the light of the above statements, choose the
correct answer from the options given below:

If V denotes the potential difference across the plates of a capacitor of capacitance C, the dimensions of $C{V^2}$ are

Velocity of light is equal to

If $L = 2.331\;cm,\;B = 2.1\;cm,$ then L+B=

In the equation X$X = 3Y{Z^2}$ X and Z have dimensions of capacitance and magnetic induction respectively. In MKS system, the dimensional formula of Y is

A physical quantity A is related to four observables a,b,c and d as follows $\;A = \frac{{{a^2}{b^3}}}{{c\sqrt d }}$ The percentage errors of measurement in a,b,c and d are 1%, 3%, 2% and 2% respectively. What is the percentage error in the quantity A?

A quantity $x$ is given by $\left(I F v^2 / W L^4\right)$ in terms of moment of inertia $I$, force $F$, velocity $v$, work $W$ and Length $L$. The dimensional formula for $x$ is same as that of :

In the relation y=r sin $\left( {\omega t - kx} \right),\;$, the dimensions of $\omega /k$ are

If C and R represent capacitance and resistance respectively then the dimensions of RC are

Unit of impulse is

If $F = 6\mathrm{\pi }{\mathrm{\eta }^\mathrm{a}}{r^b}{v^c}$ Where F=viscous force
$\mathrm{\eta }$= coefficient of viscosity
r= radius of spherical body
v= terminal velocity of the body.
Find the values of a,b and c.

A Vernier Calipers has 1mm marks on the main scale. It has 20 equal divisions on the Vernier scale which match with 16 main scale divisions. For this Vernier calipers, the least count is

$A, B, C$ and $D$ are four different physical quantities having different dimensions. None of them is dimensionless. But we know that the equation $\mathrm{AD}=\mathrm{C} \ln (\mathrm{BD})$ holds true. Then which of the combination is not a meaningful quantity?

Assertion : $\sqrt{\frac{\text { Modulus of elasticity }}{\text { Density }}}$ has the unit $\mathrm{ms}^{-1} \text {. }$

Reason: Acceleration has the dimensions of $\frac{1}{\left(\sqrt{\varepsilon_0 \mu_0}\right) t} \text {. }$