Units & measurements practice · Medium

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 45th 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 25th division coincides with the main scale line?

Assertion: The dimensional formula for product of resistance and conductance is same as for dielectric constant.

Reason: Both have dimensions of time constant.

Age of the universe is about $10^{10} \mathrm{yr}$, whereas the mankind has existed for $10^6 \mathrm{yr}$. For how many seconds would the man have existed, if age of universe were 1 day?

In the expression for Boyle's law, the product '$P V$' has dimensions of

Dimension of R is

The volume of a cube in ${m}^3$ is equal to the surface area of the cube in ${m}^2$. The volume of the cube is

Assertion: One radian is the angle subtended at the centre of circle by an arc equal in length to the radius fo the circle.
Reason: Radian is the unit of distance

Assertion: Force can be subtracted from momentum.
Reason : Physical quantities with different nature and dimensions can be subtracted.

The position of a particle at time t is given by the relation $x\left( t \right) = \left( {\frac{{{v_0}}}{\alpha }} \right)\left( {1 - {c^{ - \alpha t}}} \right)$, where ${v_0}$ is a constant and $\alpha > 0$. The diemensions of ${v_0}$ and $\alpha$ are respectively

The expression $\left[ {\mathrm{M}{\mathrm{L}^{ - 1}}{\mathrm{T}^{ - 1}}} \right]$ represents

A stone weighs $(10.0 \pm 0.1) \mathrm{kg}$ in air. The weight of the stone in water is $(5.0 \pm 0.1) \mathrm{kg}$. Find the maximum percentage error in the measurement of specific gravity.

A screw gauge of pitch $0.5 \mathrm{~mm}$ is used to measure the diameter of uniform wire of length $6.8 \mathrm{~cm}$, the main scale reading is $1.5 \mathrm{~mm}$ and circular scale reading is 7 . The calculated curved surface area of wire to appropriate significant figures is :
[Screw gauge has 50 divisions on its circular scale]

If the units of $M, L$ are doubled then the unit of kinetic energy will become:

The ratio between pico and giga is

In SI units, the dimensions of $\sqrt {\frac{{{ \in _0}}}{{{\mu _0}}}}$ is

Which of the following sets have different dimensions?

If the length of rod A is $\left( {3.25\; \pm 0.01} \right)\;\mathrm{cm}$ and that of B is $\left( {4.19\; \pm 0.01} \right)\mathrm{\;cm},$, then the rod B is longer than rod A by

From the dimensional consideration, which of the following equation is correct

Assertion: The number 1.202 has four significant figures and the number 0.0024 has two significant figures.
Reason: All the non-zero digits are significant.

If $x = at + \frac{1}{2}b{t^2}$, where ‘x’ is in metre and ‘t’ in second. Then unit of ‘b’ is?

Given below are two statement :

Statements I : Astronomical unit (Au), Parsec (Pc) and Light year (ly) are units for measuring astronomical distances.

Statements II : Au < Parsec (Pc) < ly

In the light of the above statements, choose the most appropriate answer from the options given below:

A force ‘F’ is applied onto a square plate of side L. If the percentage error in determining L is 2% and that in F is 4%, then the percentage error in pressure is