Units, Dimensions & Errors · JEE Main previous year questions

A screw gauge with a pitch of 0.5 mm and a circular scale with 50 divisions is used to measure the thickness of a thin sheet of Aluminium. Before starting the measurement, it is found that when the two jaws of the screw gauge are brought in contact, the $45^{\mathrm{th}}$ division coincides with the main scale line and that the zero of the main scale is barely visible. What is the thickness of the sheet if the main scale reading is 0.5 mm and the $25^{\mathrm{th}}$ division coincides with the main scale line?

1. A.$0.70\mathrm{mm}$
2. B.$0.50\mathrm{mm}$
3. C.$0.75\mathrm{mm}$
4. D.$0.80\mathrm{mm}$

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

1. A.$5.3200\mathrm{cm}$
2. B.$5.3\mathrm{cm}$
3. C.$5.32\mathrm{cm}$
4. D.$5.320\mathrm{cm}$

Given that $K=$ energy, $V=$ velocity, $T=$ time. If they are chosen as the fundamental units, then what is dimensional formula for surface tension?

1. A.$[K{V}^{-2}{T}^{-2}]$
2. B.$[K^2{V}^2{T}^{-2}]$
3. C.$[K^2{V}^{-2}{T}^{-2}]$
4. D.$[K{V}^2{T}^2]$

The respective number of significant figures for the numbers 23.023, 0.0003 and $2.1\times 10^{-3}$ are

1. A.5, 1, 2
2. B.5, 1, 5
3. C.5, 5, 2
4. D.4, 4, 2

1. A.$0.4\mathrm{N}\mathrm{s}$
2. B.$0.8\mathrm{N}\mathrm{s}$
3. C.$1.6\mathrm{N}\mathrm{s}$
4. D.$0.2\mathrm{N}\mathrm{s}$

In an experiment the angles are required to be measured using an instrument, 29 divisions of the main scale exactly coincide with the 30 divisions of the vernier scale. If the smallest division of the main scale is half-a degree($=0.5^{\circ }$), then the least count of the instrument is:

1. A.one minute
2. B.half minute
3. C.one degree
4. D.half degree

Which of the following units denotes the dimension $\frac{M{L}^2}{Q^2}$, where $Q$ denotes the electric charge?

1. A.$Wb/{\mathrm{m}}^2$
2. B.Henry ($H$)
3. C.$H/{\mathrm{m}}^2$
4. D.Weber ($\mathrm{Wb}$)

The ${}^{\prime }ra{d}^{\prime }$ is the correct unit used to report the measurement of

1. A.the ability of a beam of gamma ray photons to produce ions in a target
2. B.the energy delivered by radiation to a target
3. C.the biological effect of radiation
4. D.the rate of decay of radioactive source

Out of the following pair, which one does NOT have identical dimensions is

1. A.angular momentum and Planck's constant
2. B.impulse and momentum
3. C.moment of inertia and moment of a force
4. D.work and torque

1. A.$\frac{3}{2}L$
2. B.$\frac{2}{3}L$
3. C.$L$
4. D.$\frac{4}{3}L$

Which one of the following represents the correct dimensions of the coefficient of viscosity?

1. A.$\mathrm{M}{\mathrm{L}}^{-1}{\mathrm{T}}^{-1}$
2. B.$\mathrm{ML}{\mathrm{T}}^{-1}$
3. C.$\mathrm{M}{\mathrm{L}}^{-1}{\mathrm{T}}^{-2}$
4. D.$\mathrm{M}{\mathrm{L}}^{-2}{\mathrm{T}}^{-2}$

Identify the pair whose dimensions are equal

1. A.torque and work
2. B.stress and energy
3. C.force and stress
4. D.force and work