Units & measurements practice · Medium

The power of lens is $P = \frac{1}{f},\;$ where f is focal length of the lens . The dimensions of power of lens are

If ${a}=8 \pm 0.08$ and ${b}=6 \pm 0.06$, Let ${x}={a}+{b}, {y}={a}-{b}, {z}={a} \times {b}$. The correct order of $\%$ error in ${x}, {y}$ and ${z}$

Identify the pair which has different dimensions

On which of the following factor universal time depends?

Dimensional formula for surface tension is

The relative density of a material of a body is found by weighing it first in air and then in water. If the weight of the body in air is $W_1=8.00 \pm 0.05 \mathrm{~N}$ and the weight in water is $W_2=6.00 \pm 0.05 \mathrm{~N}$, then the relative density $\rho_r=W_1 /\left(W_1-W_2\right)$ with the maximum permissible error is

A student measured the diameter of a wire using a screw gauge with the least count $0.001 \mathrm{~cm}$ and listed the measurements. The measured value should be recorded as

Which one has the dimensions different from the remaining three

The unit of physical quantity obtained by the line intergral of electric field is

The dimensions of $1/2\,\varepsilon {E^2}$ are same as

Dimension of $\frac{1}{\mu_{0} \varepsilon_{0}}$ should be equal to

An atomic clock makes use of

Assertion : Parallax method cannot be used for measuring
distances of stars more than 100 light years away.
Reason : Because parallax angle reduces so much that it
cannot be measured accurately.

The dimensions of pressure is equal to

If $E$, $L$, $M$ and $G$ denote the quantities as energy, angular momentum, mass and constant of gravitation respectively, then the dimension of $P$ in the formula $P = E{L^2}{M^{ - 5}}{G^{ - 2}}$ is

In the eqn. $\left(\mathrm{P}+\frac{\mathrm{a}}{\mathrm{V}^2}\right)(\mathrm{V}-\mathrm{b})=$ constant, the unit of $\mathrm{a}$ is

Force $F$ is given in terms of time $t$ and distance $x$ by $F = a\sin ct + b\cos \,dx$, then the dimension of $a/b$ is:-

The number of significant figures in 0.235041 are

Which does not have the same unit as others

The lengths of two cylindrical rods are measured as $\ell_1=(5.62 \pm 0.01) \mathrm{cm}$ and $\ell_2=(4.34 \pm 0.02) \mathrm{cm}$. What is maximum percentage error in measurement of difference of lengths of two cylinders?

Given that $2l\sqrt {\frac{m}{T}}$, where l is the length of a string of linear density m, under tension T has the same dimensional formula as that of

SI unit of Bohr magneton is

A physical quantity is given by $X = {M^a}{L^b}{T^c}$. The percentage error in measurement of M,L and T are $\alpha ,\;\beta$ and $\gamma$ respectively. The maximum percentage error in the quantity X is

The fundamental physical quantities that have same dimensions in the dimensional formulae of torque and angular momentum are

Assertion: SI units are logical and coherent.

Reason: SI system of units is a rationalised system.

Which of the following pairs of physical quantities does not have same dimensional formulae?

Which one of the following pairs of quantities and their unit is properly matched?

In a new system of units, the net force applied on a block of mass $10 \mathrm{~kg}$ moving with acceleration $10 \mathrm{~m} / \mathrm{s}^2$ is given as 100 unit of force. When the same block is moving at a speed of $20 \mathrm{~m} / \mathrm{s}$, its kinetic energy become 20 unit of energy. A liquid has a surface tension of 10 SI units. What is the magnitude of its surface tension in new system? (Dimensional formula of surface tension is $M L^0 T^{-2}$.)

Wave number has the dimensions of

Two quantities A and B have different dimensions. Which mathematical operation given below is physically meaningful