Units & Measurement · Physics · NEET

Consider that $\sigma_s, k_B, b$ represents Stefan-Boltzmann constant, Boltzmann constant and Wien's displacement law constant, respectively. The dimension of $\sigma_s k_B^{-1} b$ is

One main scale division of a Vernier calliper is equal to 1 mm and the number of divisions on the Vernier scale is 10 . When both the jaws touch each other, the Vernier scale shifts to the left of zero of the main scale in such a way that $4^{\text {th }}$ Vernier division coincides with a division of the main scale. If this Vernier calliper measures the length of the wire to be 1 cm , the actual length of the wire is :

The speed of light in vacuum is taken as unity. If light takes 6 min 40 s to reach the Earth from the Sun, the distance between the Sun and the Earth in new unit is:

Each side of a metallic cube of mass 5.580 kg is measured to the 9.0 cm . Keeping the significant figures in view, the density of the material of the cube can be best expressed as $X \times 10^3 \mathrm{~kg} \mathrm{~m}^{-3}$ where the value of $X$ is:

In a vernier calliper, 20 VSD coincide with 16 MSD (each division of length 1 mm ). The least count of the vernier callipers is:

A balloon is made of a material of surface tension $S$ and its inflation outlet (from where gas is filled in it) has small area $A$. It is filled with a gas of density $\rho$ and takes a spherical shape of radius $R$. When the gas is allowed to flow freely out of it, its radius $r$ changes from $R$ to 0 (zero) in time $T$. If the speed $v(r)$ of gas coming out of the balloon depends on $r$ as $r^\alpha$ and $T \propto S^\alpha A^\beta \rho^\gamma R^\delta$ then

A physical quantity $P$ is related to four observations $a, b, c$ and $d$ as follows:

$$P=a^3 b^2 / c \sqrt{d}$$

The percentage errors of measurement in $a, b, c$ and $d$ are $1 \%, 3 \%, 2 \%$, and $4 \%$ respectively. The percentage error in the quantity $P$ is

Consider the diameter of a spherical object being measured with the help of a Vernier callipers. Suppose its 10 Vernier Scale Divisions (V.S.D.) are equal to its 9 Main Scale Divisions (M.S.D.). The least division in the M.S. is 0.1 cm and the zero of V.S. is at $x=0.1 \mathrm{~cm}$ when the jaws of Vernier callipers are closed. If the main scale reading for the diameter is $M=5 \mathrm{~cm}$ and the number of coinciding vernier division is 8 , the measured diameter after zero error correction, is

In an electrical circuit, the voltage is measured as $$V=(200 \pm 4)$$ volt and the current is measured as $$I=(20 \pm 0.2)$$ A. The value of the resistance is:

The pitch of an error free screw gauge is $$1 \mathrm{~mm}$$ and there are 100 divisions on the circular scale. While measuring the diameter of a thick wire, the pitch scale reads $$1 \mathrm{~mm}$$ and $$63^{\text {rd }}$$ division on the circular scale coincides with the reference line. The diameter of the wire is:

The potential energy of a particle moving along $$x$$-direction varies as $$V=\frac{A x^2}{\sqrt{x}+B}$$. The dimensions of $$\frac{A^2}{B}$$ are:

In a vernier callipers, $$(N+1)$$ divisions of vernier scale coincide with $$N$$ divisions of main scale. If $$1 \mathrm{~MSD}$$ represents $$0.1 \mathrm{~mm}$$, the vernier constant (in $$\mathrm{cm}$$) is:

The quantities which have the same dimensions as those of solid angle are:

A force defined by $$F=\alpha t^2+\beta t$$ acts on a particle at a given time $$t$$. The factor which is dimensionless, if $$\alpha$$ and $$\beta$$ are constants, is:

The diameter of a spherical bob, when measured with vernier callipers yielded the following values : $$3.33 \mathrm{~cm}, 3.32 \mathrm{~cm}, 3.34 \mathrm{~cm}, 3.33 \mathrm{~cm}$$ and $$3.32 \mathrm{~cm}$$. The mean diameter to appropriate significant figures is :

The mechanical quantity, which has dimensions of reciprocal of mass $$(\mathrm{M}^{-1})$$ is :

The errors in the measurement which arise due to unpredictable fluctuations in temperature and voltage supply are :

A metal wire has mass $$(0.4 \pm 0.002) ~\mathrm{g}$$, radius $$(0.3 \pm 0.001) ~\mathrm{mm}$$ and length $$(5 \pm 0.02) ~\mathrm{cm}$$. The maximum possible percentage error in the measurement of density will nearly be :

The physical quantity that has the same dimensional formula as pressure is

The percentage error in the measurement of g is : (Given that $$g = {{4{\pi ^2}L} \over {{T^2}}}$$, $$L = (10\, \pm \,0.1)$$ cm, $$T = (100\, \pm \,1)$$ s)

The dimensions [MLT^$$-$$2A^$$-$$2] belong to the

Plane angle and solid angle have

The area of a rectangular field (in m²) of length 55.3 m and breadth 25 m after rounding off the value for correct significant digits is