Units & measurements practice · Hard

Pressure gradient has the same dimension as that of

If the time period (T) of vibration of a liquid drop depends on surface tension (S), radius (r) of the drop and density ($\rho$) of the liquid, then the expression of T is

The length of a simple pendulum is about 100 cm known to an accuracy of 1 mm. Its period of oscillation is 2s determined by measuring the time for 100 oscillations using a clock of 0.1 s resolution. What is the accuracy in the determined value of g?

The potential energy of a particle varies with distance x from a fixed origin as $U = \left( {\frac{{A\sqrt X }}{{x + B}}} \right);$; where A and B are constants. The dimensions of AB are

To determine refractive index of glass also using
a travelling microscope, minimum number of
readings required are

A body travels uniformly a distance of $(20.0 \pm 0.2)\,m$ in time $(4.0 \pm 0.04)\,s$. The velocity of the body is

The vernier scale of a callipers is divided into 20 divisions which coincide with 18 main scale divisions. Each main scale division is 0.2 mm. The least count of the instrument is

If $x = \frac{{{A^2}{B^3}}}{{C\sqrt D }}$ and percentage errors in A, B, C & D are 1%, 2%, 3% and 4% respectively, the percentage error in $x$ is

The mass of the liquid flowing per second per unit area of cross-section of the tube is proportional to (pressure difference across the ends) $^n$ and (average velocity $^m$ of the liquid. Which one of the following relation is correct?

If force (F) , length (L) and time (T) are assumed to be fundamental units, then the dimensional formula of the mass will be

Velocity of sound in a medium is given by ${A^{1/2}}\,{d^{ - 1/2}}$ where $d$ is density of medium. Then $A$ represents

The expression for centripetal force depends upon mass of body, speed of the body and the radius of circular path. Find the expression for centripetal force

A resistor of 4 kΩ with tolerance 10% is connected in parallel with a resistor of 6 kW with tolerance 100%. The tolerance of the parallel combination is nearly

If ${L_1} = (2.02 \pm 0.01)\,m$ and ${L_2} = (1.02 \pm 0.01)\,m$ then ${L_1} + 2{L_2}$ is (in m)

If pressure P, velocity V and time T are taken as fundamental physical quantities, the dimensional formulae of the force is

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

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.

In finding out refractive index of glass slab the following observations were made through travelling microscope 50 vernier scale division = 49 MSD; 20 divisions on main scale in each $\mathrm{cm}$
For mark on paper
$\mathrm{MSR}=8.45 \mathrm{~cm}, \mathrm{VC}=26$
For mark on paper seen through slab
$\mathrm{MSR}=7.12 \mathrm{~cm}, \mathrm{VC}=41$
For powder particle on the top surface of the glass slab
$\operatorname{MSR}=4.05 \mathrm{~cm}, \mathrm{VC}=1$
$(\mathrm{MSR}=$ Main Scale Reading, $\mathrm{VC}=$ Vernier Coincidence)
Refractive index of the glass slab is:

In the relation $p = \frac{\mathrm{\alpha }}{\mathrm{\beta }}\mathrm{\;}{\mathrm{e}^{ - \frac{{\alpha z}}{{k\mathrm{\theta }}}}},\mathrm{\;}p$ , is the pressure, z the distance, k is Boltzmann constant and $\theta$ is the temperature, the dimensional formula of $\beta$ will be

The period of oscillation of a simple pendulum in the experiment is recorded as 2.63 s, 2.56 s, 2.42 s, 2.71 s and 2.80 s respectively. The average absolute error is

Expression for time in terms of G (universal gravitational constant), h (Plank’s constant) and c (speed of light) is proportional to

The liquid drop of density $\rho ,$ radius $r$ and surface tension $\sigma$ oscillates with time period T. Which of the following expression for ${T^2}$ is correct

The least count of the main scale of a vernier callipers is 1 mm. Its vernier scale is divided into 10th division and coincide with 9th division of the main scale. When jaws are touching each other, the 7th division of vernier scale coincides with a division of main scale and the zero of vernier scale is lying right side of the zero of main scale. When this vernier is used to measure length of a cylinder the zero of the vernier scale lies between 3.1 cm and 3.2 cm and 4th VSD coincides with a main scale division. The length of the cylinder is (VSD is vernier scale division)

Three identical spheres of mass 'm', are placed at the vertices of an equilateral triangle of length 'a'. When released, they interact only through gravitational force and collide after a time T = 4 seconds. If the sides of the triangle are increased to length '2a' and also the masses of the spheres are made '2m', then they will collide after _____ seconds.

The velocity v of water waves may depend on their wavelength ($\lambda$), the density of water ($\rho$) and the acceleration due to gravity (g). The method of dimensions gives the relation between these quantities as

The value of two resistors are ${R_1} = (6 \pm 0.3)k\,\Omega$ and ${R_2} = (10 \pm 0.2)k\,\Omega.$ The percentage error in the equivalent resistance when they are connected in parallel is

The speed (v) of ripples on the surface of water depends on surface tension ($\sigma$), density ($\rho$) and wavelength ($\lambda$). The square of speed (v) is proportional to

Given a charge $q,$ current $I$ and permeability of vacuum $\mu_0.$ Which of the following quantity has the dimension of momentum?

In the determination of Young’s modulus $\left( {Y = \frac{{4\;MLg}}{{\pi \;\ell {d^2}}}} \right)$ by using Searle’s method, a wire of length L=2m and diameter d=0.5mm is used. For a load M=2.5 kg, an extension $\ell = 0.25mm$ in the length of the wire is observed. Quantities d and $\ell$ are measured using a screw gauge and a micrometer, respectively. They have the same pitch of 0.5 mm. The number of divisions on their circular scale is 100. The contributions to the maximum probable scale is 100. The contributions to the maximum probable error of the Y measurement

There are atomic clocks capable of measuring time with an accuracy of 1 part in ${10^{11}}$. If two such clocks are operated with precision, then after running for 5000 years, these will record