Units & Measurements — Page 4 | NEET Physics

Q31

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 :

A

3.328 \mathrm{~cm}

B

3.3 \mathrm{~cm}

C

3.33 \mathrm{~cm}

D

3.32 \mathrm{~cm}

Correct Answer

Option C

Solution

\\text{ } \\begin{aligned} \\text{ Mean diameter } & =\\frac{\\mathrm{d}_1+\\mathrm{d}_2+\\mathrm{d}_3+\\mathrm{d}_4+\\mathrm{d}_5}{5} \\ & =\\frac{3.33+3.32+3.34+3.33+3.32}{5} \\ & =3.328 \\approx 3.33 \\end{aligned}

Q32

The mechanical quantity, which has dimensions of reciprocal of mass

(\\mathrm{M}^{-1})

is :

A angular momentum

B coefficient of thermal conductivity

C torque

D gravitational constant

Correct Answer

Option D

Solution

Angular momentum

=\\left[\\mathrm{ML}^2 \\mathrm{~T}^{-1}\\right]

Coeff of thermal conductivity

=\\left[\\mathrm{MLT}^{-3} \\mathrm{~K}^{-1}\\right]

Torque

=\\left[\\mathrm{ML}^2 \\mathrm{~T}^{-2}\\right]

Gravitational constant

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

So, gravitational constant has power of

(-1)

of

\\mathrm{M}

.

Q33

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

A Personal errors

B Least count errors

C Random errors

D Instrumental errors

Correct Answer

Option C

Solution

Error arise due to unpredictable fluctuation in temperature and voltage supply are $\\rightarrow$ random errors.

Q34

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 :

A 1.3%

B 1.6%

C 1.4%

D 1.2%

Correct Answer

Option B

Solution

\\rho=\\frac{M}{V}

\\rho=\\frac{M}{\\pi r^{2} \\ell}

\\frac{\\Delta \\rho}{\\rho}=\\frac{\\Delta \\mathrm{M}}{\\mathrm{M}}+\\frac{2 \\Delta \\mathrm{r}}{\\mathrm{r}}+\\frac{\\Delta \\ell}{\\ell}

\\frac{\\Delta \\rho}{\\rho} \\%=\\left[\\frac{0.002}{0.4}+\\frac{2(0.001)}{(0.3)}+\\frac{0.02}{5}\\right] \\times 100 \\%

=\\frac{1}{2} \\%+\\frac{2}{3} \\%+\\frac{2}{5} \\%

=1.6 \\%

Q35

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

A Coefficient of viscosity

B Force

C Momentum

D Young's modulus of elasticity

Correct Answer

Option D

Solution

Pressure

[P] = \\left[ {{F \\over A}} \\right] = \\left[ {{{ML{T^{ - 2}}} \\over {{L^2}}}} \\right] = [M{L^{ - 1}}{T^{ - 2}}]

And, dimensions of Young's modulus

[Y] = \\left[ {{{Stress} \\over {Strain}}} \\right] = [M{L^{ - 1}}{T^{ - 2}}]

[Force]

= [ML{T^{ - 2}}]

[Momentum]

= [ML{T^{ - 1}}]

[Coefficient of viscosity]

= [M{L^{ - 1}}{T^{ - 1}}]

Q36

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)

A 7%

B 2%

C 5%

D 3%

Correct Answer

Option D

Solution

Given

g = {{4{p^2}L} \\over {{T^2}}}

Fractional error in value of g

{{\\Delta g} \\over g} = {{\\Delta L} \\over L} + 2{{\\Delta T} \\over T}

\\Rightarrow {{\\Delta g} \\over g} \\times 100 = {{\\Delta L} \\over L} \\times 100 + 2{{\\Delta T} \\over T} \\times 100

\\Rightarrow {{\\Delta g} \\over g} \\times 100 = {{0.1} \\over {10}} \\times 100 + 2 \\times {1 \\over {100}} \\times 100 = 3\\%

Hence, percentage error in measurement of g is 3%

Q37

The dimensions [MLT

-

2 A

-

2 ] belong to the

A Magnetic flux

B Self inductance

C Magnetic permeability

D Electric permittivity

Correct Answer

Option C

Solution

Dimensional formula of magnetic permeability is [MLT $-$ 2 A $-$ 2 ]

Q38

Plane angle and solid angle have

A Units but no dimensions

B Dimensions but no units

C No units and no dimensions

D Both units and dimensions

Correct Answer

Option A

Solution

Plane angle =

{{Arc} \\over {Radius}} = {{[L]} \\over {[L]}}\\overset{{} \}\\longrightarrow

Unit = Radian

= [{M^0}{L^0}{T^0}]

Solid angle =

{{Area} \\over {{{(Radius)}^2}}}\\overset{{} \}\\longrightarrow

Unit = Steradian

= {{{L^2}} \\over {{L^2}}} = [{M^0}{L^0}{T^0}]

$\\therefore$ Both have units but no dimensions.

Q39

The area of a rectangular field (in m 2 ) of length 55.3 m and breadth 25 m after rounding off the value for correct significant digits is

A 138

\times

10 1

B 1382

C 1382.5

D 14

\times

10 2

Correct Answer

Option D

Solution

Area = Length $\\times$ Breadth = 55.3 $\\times$ 25 m 2 = 1382.5 m 2 = 14 $\\times$ 10 2 m 2 (Rounding off of two significant figures)

Q40

The E and G respectively denote energy and gravitational constant, then

{E \\over G}

has the dimensions of :

A [M 2 ] [L

-

2 ] [T

-

1 ]

B [M 2 ] [L

-

1 ] [T 0 ]

C [M] [L

-

1 ] [T

-

1 ]

D [M] [L 0 ] [T 0 ]

Correct Answer

Option B

Solution

E = energy = [ML 2 T $-$ 2 ] G = Gravitational constant = [M $-$ 1 L 3 T $-$ 2 ] So,

{E \\over G} = {{[E]} \\over {[G]}} = {{M{L^2}{T^{ - 2}}} \\over {{M^{ - 1}}{L^3}{T^{ - 2}}}} = [{M^2}{L^{ - 1}}{T^0}]