Units & measurements practice · Mixed difficulty

The equation of a circle is given by $x^2+y^2=a^2$, where $a$ is the radius. If the equation is modified to change the origin other than $(0,0)$, then find out the correct dimensions of $A$ and $B$ in a new equation $(x-A t)^2+\left(y-\frac{t}{B}\right)^2=a^2$. The dimension of $t$ is given as $\left[\mathrm{T}^{-1}\right]$.

An athletic coach told his team that muscle times speed equals power. What dimensions does he view for muscle

A spherical body of mass $m$ and radius $r$ is allowed to fall in a medium of viscosity $\eta$. The time in which the velocity of the body increases from zero to 0.63 times the terminal velocity $(v)$ is called time constant ( $\tau)$. Dimensionally $\tau$ can be represented by

The dimensions of the quantity $\frac{ L }{ RCV }$ are - ( L-inductance, R-resitance, C-capacitance and V-potential difference)

Using mass $(M)$, length $(L)$, time $(T)$ and current $(A)$ as fundamental quantities, the dimensions of permeability are

One centimetre on the main scale of a vernier callipers is divided into 10 equal parts. If 10 divisions of vernier coincide with 8 small divisions of the main scale, the least count of vernier callipers is

If the error in the measurement of momentum of a particle is $100 \%$ then the error in the measurement of kinetic energy would be

The diameter and height of a cylinder are measured by a meter scale to be $12.6\, \pm \,0.1\,cm$ and $34.2\, \pm \,0.1\,cm$, respectively. What will be the value of tis Volume in appropriate significant figures?

Which of the following is not the unit of time?

The pitch of a screw gauge $15 {~mm}$ and there are 100 divisions on the circular scale. While measuring diameter of a thick wire. The pitch scale reads $1 {~mm}$ and 63 rad division on the circular scale coincides with the reference. The length of the wire is $5.6 {~cm}$, then which one of the following option is correct?

Crane is British unit of volume (one crane = 170.4742). convert crane into SI units.

What is dimensional formula of thermal conductivity?

One yard in SI units is equal

Assertion: The quantity $\left(1 / \sqrt{\mu_0 \varepsilon_0}\right)$ is dimensionally equal to velocity and numerically equal to velocity of light.

Reason: $\mu_0$ is permeability of free space and $\varepsilon_0$ is the permittivity of free space.

Statement I: The mass of an object is $13.2 \mathrm{~kg}$ in the measurement there are 3 significant figures.

Statement II: The same mass when expressed in grams as $13200 \mathrm{~g}$ has five significant figures.

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

Which of the following five physical parameters have the same dimensions (A) Energy density (B) Refractive index (C) Dielectric constant (D) Young’s modulus (E) Magnetic field

Assertion: Light year is the distance that light travels with velocity of $3 \times 10^8 \mathrm{~ms}^{-1}$ in one year.
Reason: Light year is the unit for measuring time.

One main scale division of a vernier caliper is equal to $m$ units. If $n^{th}$ division of main scale coincides with $({n}+1)^{th}$ division of vernier scale, the least count of the vernier caliper is:

The dimensional formula for areal velocity is

Number of significant figures in expression $\frac{{4.327\,g}}{{2.51\,c{m^{.3}}}}$ is

Which of the following functions of $A$ and $B$ is possibly correct if $A$ and $B$ possess different dimensions?

The dimension of kinetic energy is same as that of

Weber is the unit of

The Richardson equation is given by $\mathrm{I}=\mathrm{AT}^2 \mathrm{e}^{-\mathrm{B} / \mathrm{kT}}$. The dimensional formula for $\mathrm{AB}^2$ is same as that for

Which pair has the same dimensions

The best method to reduce random error is

Two physical quantities have same dimensions then their magnitude;

Which of the following measurements is most accurate?

The number of significant figures in a number
"1700.00200" is