Units & measurements practice · Mixed difficulty

Applying the principle of homogeneity of dimensions, determine which one is correct. where $\mathrm{T}$ is time period, $\mathrm{G}$ is gravitational constant, $\mathrm{M}$ is mass, $\mathrm{r}$ is radius of orbit.

What is the use of thin strip at the back of Vernier caliper?

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

Size of universe is about

The density of a material in CGS system is $2 \mathrm{~g} / \mathrm{cm}^3$. In a system of units in which unit of length is $2 \mathrm{~cm}$ and unit of mass is $4 \mathrm{~g}$, what is the numerical value of the density of the material?

Which is dimensionless?

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

A student measures the distance traversed in free fall of a body, initially at rest in a given time. He uses this data to estimate g, the acceleration due to gravity. If the maximum percentage errors in measurement of the distance and the time are ${e_1}$ and ${e_2}$ respectively, the percentage error in the estimation of g is

The specific resistance ρ of a circular wire of radius r. Resistance R and and length l is given by $\rho = \frac{{\mathrm{\pi }{r^2}R}}{l}.$ Given, $r = 0:\left( {24 \pm 0.02} \right)cm,\,R = \left( {30 \pm 1} \right)\mathrm{\Omega }$ and $l = \left( {4.80 \pm 0.01} \right)cm.$ The percentage error in ρ is nearly

The dimensions of power are

If the unit of length is 4 m and that of velocity is $6\,m{s^{ - 1}},$ the unit of time is (in second)

With the usual notations, the following equation ${S_t} = u + \frac{1}{2}a\left( {2t - 1} \right)\;$ is

If $S = \frac{1}{3}f{t^3},f$ has the dimensions of

Identify the pair whose dimensions are equal.

We can reduce random errors by

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)

The dimensions of power are

If $x = a - b$, then the maximum percentage error in the measurement of x will be

What are the units of $K = 1/4\pi {\varepsilon _0}$

Ampere-hour is a unit of

If error in radius is 3%, what is error in volume of sphere?

The dimensional formula for impulse is

Which of the following is the smallest unit

Instrumental error can be caused due 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 :

The physical quantity having the dimensions $\left[ {{\mathrm{M}^{ - 1}}{\mathrm{L}^{ - 3}}{\mathrm{A}^2}{T^3}} \right]$ is

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

A spectrometer gives the following reading when used to measure the angle of a prism Main scale reading : 58.5 degree Vernier scale reading : 09 divisions Given that 1 division on main scale corresponds to 0.5 degree. Total divisions on the vernier scale is 30 and match with 29 divisions of the main scale. The angle of the prism from the above data

The number of significant figures in the numbers $4.8000 \times {10^4}$ and 48000.50 are respectively