A public park, in the form of a square, has an area of $\left( {100 \pm 0.2} \right){{\rm{m}}^2}$ . The side of park is

$\left( {10.0 \pm 0.1} \right)m$

A screw gauge has least count of ${\rm{0}}{\rm{.01 mm}}$ and there are ${\rm{50}}$ divisions in its circular scale. The pitch of the screw gauge is :

${\rm{0}}{\rm{.5}}\,\,{\rm{mm}}$

${\rm{0}}{\rm{.01}}\,\,{\rm{mm}}$

${\rm{0}}{\rm{.25}}\,\,{\rm{mm}}$

${\rm{1}}{\rm{.0}}\,\,{\rm{mm}}$

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

$\left( {0.94{\rm{\;}} \pm 0.02} \right){\rm{\;cm}}$

$\left( {0.94{\rm{\;}} \pm 0.00} \right){\rm{\;cm}}$

$\left( {0.94{\rm{\;}} \pm 0.01} \right){\rm{\;cm}}$

$\left( {0.94{\rm{\;}} \pm 0.005} \right){\rm{\;cm}}$

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NEET • PHYSICS • UNITS & MEASUREMENTS

Units & measurements practice · Medium

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Showing 1-30 of 210 questions

1 Medium

1 of 210

Application +4 | -1

An object is moving through the liquid. The viscous damping force acting on it is proportional to the velocity. Then dimension of constant of proportionality is

View answer and explanation

Correct option: D

M{L^0}{T^{ - 1}}

Option D (

M{L^0}{T^{ - 1}}

) is correct because the viscous force is proportional to velocity, so the constant of proportionality has dimensions of mass/time.

2 Medium

2 of 210

Remembering +4 | -1

The error due to parallax is a:

View answer and explanation

Correct option: C

Personal error

Option C (Personal error) is correct because parallax error arises from the observer's position and judgment while taking readings.

3 Medium

3 of 210

Understanding +4 | -1

The dimensional formula of self-inductance is

View answer and explanation

Correct option: C

\left[ {\mathrm{M}{\mathrm{L}^2}{\mathrm{T}^{ - 2}}{\mathrm{A}^{ - 2}}} \right]

Option C (

\left[ {\mathrm{M}{\mathrm{L}^2}{\mathrm{T}^{ - 2}}{\mathrm{A}^{ - 2}}} \right]

) is correct because self-inductance is related to energy stored in a magnetic field, and its dimensions can be derived from that.

4 Medium

4 of 210

Understanding +4 | -1

The dimension of

\frac{1}{{\sqrt {{\varepsilon _0}{\mu _0}} }}

is that of

View answer and explanation

Correct option: A

Velocity

Option A (Velocity) is correct because

\frac{1}{{\sqrt {{\varepsilon _0}{\mu _0}} }}

represents the speed of light, which has the dimensions of velocity.

5 Medium

5 of 210

Analyzing +4 | -1

Which is wrong dimension

View answer and explanation

Correct option: B

\mathrm{s}=\mathrm{vt}^2

Option B (

\mathrm{s}=\mathrm{vt}^2

) is wrong dimensionally because the dimensions on the left side (length) do not match the dimensions on the right side (length × time).

6 Medium

6 of 210

Application +4 | -1

The dimensional formula of capacitance in terms of M,L,T and I is

View answer and explanation

Correct option: D

\left[ {{\mathrm{M}^{ - 1}}{\mathrm{L}^{ - 2}}{\mathrm{T}^4}{\mathrm{I}^2}} \right]

Option D

\left[ {{\mathrm{M}^{ - 1}}{\mathrm{L}^{ - 2}}{\mathrm{T}^4}{\mathrm{I}^2}} \right]

is correct because it is derived from the formula for capacitance and the dimensional formulas for charge, voltage, and current.

7 Medium

7 of 210

Application +4 | -1

The length

l,

, breadth b and thickness t of a block are measured with the help of a metre scale. Given

l = 15.12 \pm 0.01

cm,

b = 10.15 \pm 0.01

cm,

t = 5.28 \pm 0.01

cm.The percentage error in volume is

View answer and explanation

Correct option: C

0.0037

Option C (0.0037) is correct because the percentage error in volume is the sum of the percentage errors in length, breadth, and thickness.

8 Medium

8 of 210

Analyzing +4 | -1

If the speed of light (c), acceleration due to gravity (g) and pressure (p) are taken as the fundamental quantities, then the dimension of gravitational constant is

View answer and explanation

Correct option: B

{c^0}{g^2}{p^{ - 1}}

Option B (

{c^0}{g^2}{p^{ - 1}}

) is correct because it provides the correct dimensions for the gravitational constant when speed of light, acceleration due to gravity, and pressure are fundamental quantities.

9 Medium

9 of 210

Application +4 | -1

A public park, in the form of a square, has an area of

\left( {100 \pm 0.2} \right){\mathrm{m}^2}

. The side of park is

View answer and explanation

Correct option: A

\left( {10 \pm 0.01} \right)m

Option A (

\left( {10 \pm 0.01} \right)m

) is correct because the side is the square root of the area, and the percentage error in the side is half the percentage error in the area.

10 Medium

10 of 210

Application +4 | -1

What is the unit of k in the relation

U = \frac{{ky}}{{{y^2} + {a^2}}}

where U represents the potential energy, y represents the displacement and a represents the maximum displacement ie, amplitude?

View answer and explanation

Correct option: C

J m

Option C (J m) is correct because from the relation

U = \frac{{ky}}{{{y^2} + {a^2}}}

, k must have the dimensions of energy times length, which corresponds to J m.

11 Medium

11 of 210

Application +4 | -1

The dimensional formula of coefficient of permittivity for free space

\left( {{\varepsilon _0}} \right)

in the equation

F = \frac{1}{{4\mathrm{\pi }{\varepsilon _0}}}\frac{{{q_1}{q_2}}}{{{r^2}}},

where symbols have their usual meanings, is

View answer and explanation

Correct option: B

\left[ {{\mathrm{M}^{ - 1}}{\mathrm{L}^{ - 3}}{\mathrm{T}^4}{\mathrm{A}^2}} \right]

Option B (

[{\mathrm{M}^{ - 1}}{\mathrm{L}^{ - 3}}{\mathrm{T}^4}{\mathrm{A}^2}]

) is correct because it correctly derives the dimensional formula of permittivity using Coulomb's law.

12 Medium

12 of 210

Analyzing +4 | -1

Assertion A: If in five complete rotations of the circular scale, the distance travelled on main scale of the screw gauge is 5 mm and there are 50 total divisions on circular scale, then least count is 0.001 cm.
Reason R: Least count =

\frac{{\mathrm{Pitch}}}{{\mathrm{Total}\,\,\mathrm{division}\,\,\mathrm{on}\,\,\mathrm{circular}\,\,\mathrm{scale}}}

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

View answer and explanation

Correct option: D

A is not correct but R is correct

Option D (A is not correct but R is correct) is correct because the assertion incorrectly calculates the least count, while the reason provides the correct formula.

13 Medium

13 of 210

Remembering +4 | -1

Unit of reduction factor is

View answer and explanation

Correct option: A

ampere

Option A (ampere) is correct because the reduction factor of a tangent galvanometer is a measure of the current required to produce a certain deflection, hence its unit is ampere.

14 Medium

14 of 210

Application +4 | -1

A screw gauge has least count of

\mathrm{0}\mathrm{.01 mm}

and there are

\mathrm{50}

divisions in its circular scale. The pitch of the screw gauge is :

View answer and explanation

Correct option: C

\mathrm{0}\mathrm{.5}\,\,\mathrm{mm}

Option C (

\mathrm{0}\mathrm{.5}\,\mathrm{mm}

) is correct because the pitch is calculated by multiplying the least count by the number of divisions on the circular scale.

15 Medium

15 of 210

Remembering +4 | -1

The dimensions of speed and velocity are

View answer and explanation

Correct option: D

\left[\mathrm{LT}^{-1}\right],\left[\mathrm{LT}^{-1}\right]

Option D ([LT^-1],[LT^-1]) is correct because both speed and velocity are defined as distance divided by time, hence having the same dimensions.

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16 Medium

16 of 210

Remembering +4 | -1

Dimensions of planck’s constant is:

View answer and explanation

Correct option: A

\left[ {{M^1}{L^2}{T^{ - 1}}} \right]

Option A (

\left[ {{M^1}{L^2}{T^{ - 1}}} \right]

) is correct because Planck's constant relates energy and frequency (E = hf), and its dimensions can be derived from the dimensions of energy and frequency.

17 Medium

17 of 210

Application +4 | -1

The surface tension of a liquid is 70 dyne/cm, in MKS system value is

View answer and explanation

Correct option: B

7 \times {10^{ - 2}}\;N/m

Option B (

7 \times {10^{ - 2}}\;N/m

) is correct because 1 dyne/cm equals

10^{-3}

N/m.

18 Medium

18 of 210

Application +4 | -1

The length, breadth and thickness of a metal block is given by

l = 90 cm

, b=8 cm, t=2.45 cm. The volume of the block is

View answer and explanation

Correct option: A

2 \times {10^2}\mathrm{c}{\mathrm{m}^3}

Option A (

2 \times {10^2}\mathrm{c}{\mathrm{m}^3}

) is correct because the volume should be rounded to the least number of significant figures among the given dimensions.

19 Medium

19 of 210

Understanding +4 | -1

\left[ {M{L^2}{T^{ - 3}}} \right]

is the dimension of

View answer and explanation

Correct option: B

Power

Option B (Power) is correct because power is work done per unit time, and its dimensional formula is

[ML^2T^{-3}]

20 Medium

20 of 210

Understanding +4 | -1

X = A \times B

and

\Delta X

and ∆A and ∆B are maximum absolute errors in X, A and B respectively, then the maximum relative error in X is given by

View answer and explanation

Correct option: D

\frac{{\Delta X}}{X} = \frac{{\Delta A}}{A} + \frac{{\Delta B}}{B}

Option D (

\frac{{\Delta X}}{X} = \frac{{\Delta A}}{A} + \frac{{\Delta B}}{B}

) is correct because the relative error in a product is the sum of the relative errors of the factors.

21 Medium

21 of 210

Analyzing +4 | -1

A quantity

y

is related to another quantity

\mathrm{x}

by the equation

\mathrm{y}=\mathrm{kx}^{\mathrm{a}}

where

\mathrm{k}

and

\mathrm{a}

are constant. If percentage error in the measurement of

x

p

, then error in

y

depends upon

View answer and explanation

Correct option: D

p, k and a all

Option C (p and a) is correct because the percentage error in y depends on the percentage error in x (p) and the exponent a, as derived from error propagation.

22 Medium

22 of 210

Analyzing +4 | -1

Surface tension has the same dimensions as that of

View answer and explanation

Correct option: D

Spring constant

Option D (Spring constant) is correct because both surface tension and spring constant have the same dimensional formula [MT⁻²].

23 Medium

23 of 210

Application +4 | -1

If P represents radiations pressure, c represents speed of light and Q represents radiation energy striking a unit area per second, the non-zero integers x,y and z such that 

{P^x}{Q^y}{c^z}

is dimensionless, are

View answer and explanation

Correct option: B

x = 1,\;y = - 1,\;z = 1

Option B (

x = 1,\;y = - 1,\;z = 1

) is correct because it involves finding the values of x, y, and z such that

{P^x}{Q^y}{c^z}

is dimensionless, where P is radiation pressure, c is the speed of light, and Q is radiation energy striking a unit area per second. By equating the dimensions to M⁰L⁰T⁰, we can solve for x, y, and z.

24 Medium

24 of 210

Understanding +4 | -1

Read the following statements and Identify the correct statement/s. A: A choice of change of different units change the number of significant digits. B: To remove ambiguities in determining the number of significant figures, the best way is to report the measurement in scientific notation. C: Solid angle made by a hemisphere at its centre is

2\pi

steradian.

View answer and explanation

Correct option: B

Only B is true

Option B (Only B is true) is correct because significant figures can change with units, scientific notation is best for clarity, and a hemisphere makes a solid angle of

2\pi

steradians.

25 Medium

25 of 210

Analyzing +4 | -1

Which one has the dimensions different from the remaining three

View answer and explanation

Correct option: A

Power

Option A (Power) is correct because Power has dimensions of [ML²T⁻³], while Work, Torque, and Energy all have dimensions of [ML²T⁻²].

26 Medium

26 of 210

Application +4 | -1

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

View answer and explanation

Correct option: C

\left( {0.94\mathrm{\;} \pm 0.02} \right)\mathrm{\;cm}

Option C (

\left( {0.94\mathrm{\;} \pm 0.02} \right)\mathrm{\;cm}

) is correct because the difference in lengths is calculated, and the errors are added.

27 Medium

27 of 210

Analyzing +4 | -1

Out of the following which pair of quantities do not have same dimensions

View answer and explanation

Correct option: D

Torque and moment of inertia

Option D (Torque and moment of inertia) is correct because torque has dimensions [ML²T⁻²] and moment of inertia has dimensions [ML²], which are different.

28 Medium

28 of 210

Analyzing +4 | -1

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

View answer and explanation

Correct option: A

{M^0}{L^1}{T^{ - 1}}\,{\text{and}}\,{T^{ - 1}}

Option A (

{M^0}{L^1}{T^{ - 1}}\,{\text{and}}\,{T^{ - 1}}

) is correct because it correctly identifies the dimensions of velocity and inverse time, respectively.

29 Medium

29 of 210

Remembering +4 | -1

If the digit to be dropped is more than 5, then the preceding digit is _____.

View answer and explanation

Correct option: A

Raised by 1

Option A (Raised by 1) is correct because this is the standard rounding rule: if the digit to be dropped is greater than 5, the preceding digit is increased by 1.

30 Medium

30 of 210

Understanding +4 | -1

State the number of significant figures in the
following:
(i) 2.000 m (ii) 5100 kg (iii) 0.050 cm.

View answer and explanation

Correct option: A

(i) - 4; (ii) - 4; (iii) - 2

Option A ((i) - 4; (ii) - 4; (iii) - 2) is correct because 2.000 has 4 significant figures, 5100 kg has 2 or 4 (ambiguous), but assuming it's measured to the nearest kg, it's 4, and 0.050 cm has 2.

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Key Takeaways

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