Units & measurements practice · Mixed difficulty

Identify the pair which has different dimensions

On which of the following factor universal time depends?

Dimensional formula for surface tension is

If $x$ is the depression produced in the middle of a beam of length $l$ breadth b and thickness d and a load of mass m is attached at the centre of the beam. If y is the young Modulus of the material. Which of the following is dimensionally correct

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

Choose the incorrect options among the following

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

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

A physical quantity $\mathrm{T}=\frac{\sqrt{\mathrm{abc}^2}}{\mathrm{~d}^3 \mathrm{e}^{1 / 6}}$ is determined by measuring a, b, c, d, e separately with the percentage error of $1 \%, 2 \%, 3 \%, 4 \%, 3 \%$ respectively. Minimum amount of error is contributed by the measurement of :

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

Pressure gradient has the same dimension as that of

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 unit of specific resistance is

The value of Planck's constant is

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?