Units Dimensions And Measurement — DPP 3

20 NEET questions from Physics and Measurement, with answers and explanations. Attempt it as a timed test to get scoring, accuracy breakdown and mistake tracking.

Attempt this test free 20 questions · 30 minutes · +80 marks
1
The force is given in terms of time (t) and displacement ( x ) by the equation :
F = A cos Bx + C sin Dt
Then, the dimensions of $\frac { D } { B }$ are :-
  1. A $\mathrm { M } ^ { \circ } \mathrm { L } ^ { \circ } \mathrm { T } ^ { \circ }$
  2. B $\mathrm { M } ^ { \circ } \mathrm { L } ^ { \circ } \mathrm { T } ^ { - 1 }$
  3. C $\mathrm { M } ^ { \circ } \mathrm { L } ^ { - 1 } \mathrm {~T} ^ { \circ }$
  4. D $\mathrm { M } ^ { \circ } \mathrm { LT } ^ { - 1 }$ PPM043
Show answer & explanation

Correct answer: D

θ in cosθ and sinθ is dimensionless
$\begin{array}{l}\mathrm{Bx}=\mathrm{M}^{0} \mathrm{~L}^{0} \mathrm{~L}^{0} \Rightarrow \mathrm{BL}^{1}=\mathrm{M}^{0} \mathrm{~L}^{0} \mathrm{~T}^{0} \Rightarrow \mathrm{~B}=\mathrm{M}^{0} \mathrm{~L}^{-1} \mathrm{~T}^{0} \\ \mathrm{Dt}=\mathrm{M}^{0} \mathrm{~L}^{0} \mathrm{~T}^{0} \Rightarrow \mathrm{DT}^{1}=\mathrm{M}^{0} \mathrm{~L}^{0} \mathrm{~T}^{0} \Rightarrow \mathrm{D}=\mathrm{M}^{0} \mathrm{~L}^{0} \mathrm{~T}^{-1} \\ \frac{\mathrm{D}}{\mathrm{B}}=\frac{\mathrm{M}^{0} \mathrm{~L}^{0} \mathrm{~T}^{-1}}{\mathrm{M}^{0} \mathrm{~L}^{-1} \mathrm{~T}^{0}}=\mathrm{L}^{1} \mathrm{~T}^{-1}\end{array}$
2
Percentage error in measuring the radius (R) and mass (M) of a solid sphere are 2% & 1% respectively. Then error in measurement of moment of inertia about to its diameter $\left( \right.$ i.e. $\left. I = \frac { 2 } { 5 } M R ^ { 2 } \right)$ is :-
  1. A 3%
  2. B 6%
  3. C 5%
  4. D 4%
Show answer & explanation

Correct answer: C

$\begin{array}{l}\mathrm{I}=2 / 5 \mathrm{MR}^{2} \\ \frac{\Delta \mathrm{I}}{\mathrm{I}}=\frac{\Delta \mathrm{M}}{\mathrm{M}}+2 \frac{\Delta \mathrm{R}}{\mathrm{R}} \\ \frac{\Delta \mathrm{I}}{\mathrm{I}} \times 100=1 \%+2 \times 2 \%=5 \%\end{array}$
3
Number of significant digits in 0.01230 is :-
  1. A 3
  2. B 4
  3. C 5
  4. D 6
Show answer

Correct answer: B

4
Which of the following physical quantities has neither dimensions nor unit?
  1. A angle
  2. B Luminous intensity
  3. C coefficient of friction
  4. D Electric current
Show answer & explanation

Correct answer: C

Coefficient of friction is unitless & dimenssionless.
5
Subtract 0.2 J from 5.27 J and express the result with correct number of significant figures :-
  1. A 5.1 J
  2. B 5.06 J
  3. C 5.0 J
  4. D 5 J
Show answer & explanation

Correct answer: A

Units Dimensions And Measurement – NEET-6098
6
After rounding off the number 4621 to 2 significant digits the value becomes :-
  1. A 4600
  2. B 4500
  3. C 4700
  4. D 4720
Show answer & explanation

Correct answer: A

4621 = 4.621 × 10$^{3}$
= 4.6 × 10$^{3}$
= 4600
7
If energy (E), velocity (v) and force (F), be taken as fundamental quantities, then what are the dimensions of mass :-
  1. A $\mathrm { EV } ^ { 2 }$
  2. B $\mathrm { EV } ^ { - 2 }$
  3. C $\mathrm { FV } ^ { - 1 }$
  4. D $\mathrm { FV } ^ { - 2 }$
Show answer & explanation

Correct answer: B

$\begin{array}{l}\mathrm{M}=\mathrm{E}^{\mathrm{a}} \mathrm{V}^{\mathrm{b}} \mathrm{F}^{\mathrm{c}} \\ {\left[\mathrm{M}^{1}\right]=\left[\mathrm{ML}^{2} \mathrm{~T}^{-2}\right]^{\mathrm{a}}\left[\mathrm{L}^{1} \mathrm{~T}^{-1}\right]^{\mathrm{b}}\left[\mathrm{M}^{1} \mathrm{~L}^{1} \mathrm{~T}^{-2}\right] \mathrm{c}} \\ {\left[\mathrm{M}^{1} \mathrm{~L}^{0} \mathrm{~T}^{0}\right]=\left[\mathrm{M}^{\mathrm{a}+\mathrm{c}} \mathrm{L}^{2 \mathrm{a}+\mathrm{b}+\mathrm{c}} \mathrm{T}^{-2 \mathrm{a}-\mathrm{b}-2 \mathrm{c}}\right]} \\ \mathrm{a}+\mathrm{c}=1 ; 2 \mathrm{a}+\mathrm{b}+\mathrm{c}=0 ;-2 \mathrm{a}-\mathrm{b}-2 \mathrm{c}=0\end{array}$
8
If y represents distance and x -represents time, dimensions of $\frac { d ^ { 2 } y } { d x ^ { 2 } }$ are :-
  1. A $\mathrm { LT } ^ { - 1 }$
  2. B $\mathrm { L } ^ { 2 } \mathrm {~T} ^ { 2 }$
  3. C $\mathrm { L } ^ { 2 } \mathrm {~T} ^ { - 1 }$
  4. D $\mathrm { LT } ^ { - 2 }$
Show answer & explanation

Correct answer: D

$\frac{\mathrm{d}^{2} \mathrm{y}}{\mathrm{dx}^{2}}=\left[\frac{\mathrm{L}^{1}}{\mathrm{~T}^{2}}\right]=\left[\mathrm{L}_{1} \mathrm{~T}^{-2}\right]$
9
If the units of length, velocity and force are half, then the units of Power will be :-
  1. A doubled
  2. B halved
  3. C one fourth
  4. D remains unaffected
Show answer & explanation

Correct answer: C

[Power] = [Force × Velocity]
so becomes one fourth
10
Which of the following has the highest number of significant figures ?
  1. A $0.007 \mathrm {~m} ^ { 2 }$
  2. B $2.64 \times 10 ^ { 24 } \mathrm {~kg}$
  3. C $0.0006032 \mathrm {~m} ^ { 2 }$
  4. D 6.3200 J
Show answer & explanation

Correct answer: D

According to the rules of significant figures
0.007 m$^{2}$ has one significant figures.
2.64 × 10$^{24}$ kg has three significant figures.
0.0006032 m$^{2}$ has four significant figures.
6.3200 J has five significant figures.
11
If f = x$^{2}$, then the relative error in f is :-
  1. A $\frac { 2 \Delta x } { x }$
  2. B $\frac { ( \Delta x ) ^ { 2 } } { x }$
  3. C $\frac { \Delta x } { x }$
  4. D $( \Delta x ) ^ { 2 }$
Show answer & explanation

Correct answer: A

f(x) = x$^{2}$
Relative error = $2\left(\frac{\Delta x}{x}\right)$
12
There is an error of 2% in the measurement of side of a cube. The percentage error in the calculation of its volume will be :-
  1. A 1%
  2. B 2%
  3. C 3%
  4. D 6%
Show answer & explanation

Correct answer: D

Volume of cube V = (side)$^{3}$
∴ V = a$^{3}$.
Take log and differentiate.
$\frac{\Delta \mathrm{V}}{\mathrm{V}} \times 100=3 \frac{\Delta \mathrm{a}}{\mathrm{a}} \times 100=3( \pm 2 \%)= \pm 6 \%$.
13
Given P = 0.0030 m, Q = 2.40 m and R = 3000 m, the number of significant figures in P , Q and R are respectively :-
  1. A 1, 2, 1
  2. B 2, 3, 4
  3. C 4, 2, 1
  4. D 4, 2, 4
Show answer & explanation

Correct answer: B

P = 0.0030 ⇒ 2 SF
Q = 2.40 ⇒ 3 SF
R = 3000 m ⇒ 4 SF
14
A system has basic dimensions as density [D], velocity [V] and area [A]. The dimensional representation of force in this system is :-
  1. A $A V ^ { 2 } D$
  2. B $A ^ { 2 } V D$
  3. C $\mathrm { AVD } ^ { 2 }$
  4. D $\mathrm { A } ^ { 0 } \mathrm { VD }$
Show answer & explanation

Correct answer: A

$\begin{array}{l}\mathrm{F}=\mathrm{D}^{\mathrm{a}} \mathrm{V}^{\mathrm{b}} \mathrm{A}^{\mathrm{c}} \\ {\left[\mathrm{M}^{1} \mathrm{~L}^{1} \mathrm{~T}^{-2}\right]=\left[\mathrm{M}^{1} \mathrm{~L}^{-3}\right]^{\mathrm{a}}\left[\mathrm{L}^{1} \mathrm{~T}^{-1}\right]^{\mathrm{b}}\left[\mathrm{L}^{2}\right]^{\mathrm{c}}} \\ {\left[\mathrm{M}^{1} \mathrm{~L}^{1} \mathrm{~T}^{-2}\right]=\left[\mathrm{M}^{\mathrm{a}} \mathrm{L}^{-3 \mathrm{a}+\mathrm{b}+2 \mathrm{c}} \mathrm{T}^{-\mathrm{b}}\right]} \\ \mathrm{a}=1 ;-3 \mathrm{a}+\mathrm{b}+2 \mathrm{c}=1 ;-\mathrm{b}=-2\end{array}$
15
When a copper sphere is heated, maximum percentage change will be observed in-
  1. A radius
  2. B area
  3. C volume
  4. D none of these
Show answer & explanation

Correct answer: C

If % change in radius = x%
then % change in area = 2x%
and % change in volume = 3x%
16
The force F , on a sphere of radius 'a' moving in a medium with velocity v is given by $\mathrm { F } = 6 \pi \eta \mathrm { av }$. The dimensions of η are :-
  1. A $\left[ \mathrm { ML } ^ { - 1 } \mathrm {~T} ^ { - 1 } \right]$
  2. B $\left[ \mathrm { MT } ^ { - 1 } \right]$
  3. C $\left[ \mathrm { MLT } ^ { - 2 } \right]$
  4. D $\left[ \mathrm { ML } ^ { - 3 } \right]$
Show answer & explanation

Correct answer: A

$\eta=\frac{\mathrm{F}}{6 \pi \mathrm{av}}=\frac{\mathrm{M}^{1} \mathrm{~L}^{1} \mathrm{~T}^{-2}}{\left[\mathrm{~L}^{1}\right]\left[\mathrm{L}^{1} \mathrm{~T}^{-1}\right]}=\mathrm{M}^{1} \mathrm{~L}^{-1} \mathrm{~T}^{-1}$
17
The percentage error in the measurement of mass and speed are 2% and 3% respectively. How much will be the maximum error in the estimate of kinetic energy obtained by measuring mass and speed :-
  1. A 11%
  2. B 8%
  3. C 5%
  4. D 4%
Show answer & explanation

Correct answer: B

$\begin{array}{l}\mathrm{KE}=\frac{1}{2} \mathrm{mv}^{2} \\ \frac{\Delta \mathrm{KE}}{\mathrm{KE}}=\frac{\Delta \mathrm{m}}{\mathrm{m}}+2 \frac{\Delta \mathrm{v}}{\mathrm{v}} \\ \frac{\Delta \mathrm{KE}}{\mathrm{KE}} \times 100=2+2 \times 3=8 \%\end{array}$
18
The external and internal radius of a hollow cylinder are measured to be $( 5.23 \pm 0.015 ) \mathrm { cm }$ and $( 4.89 \pm 0.005 ) \mathrm { cm }$. The thickness of the wall of the cylinder is :-
  1. A $( 0.34 \pm 0.02 ) \mathrm { cm }$
  2. B $( 0.17 \pm 0.02 ) \mathrm { cm }$
  3. C $( 0.17 \pm 0.01 ) \mathrm { cm }$
  4. D $( 0.34 \pm 0.01 ) \mathrm { cm }$
Show answer & explanation

Correct answer: A

Thickness of cylinder can be written as
$\begin{array}{l}\mathrm{t}=\mathrm{t} \pm \Delta \mathrm{t} \\ \mathrm{t}=\mathrm{r}_{2}-\mathrm{r}_{1}=5.23-4.89=0.34 \\ \Delta \mathrm{t}=\Delta \mathrm{r}_{1}+\Delta \mathrm{r}_{2}=0.015+0.005=0.02 \\ \mathrm{t}=(0.34 \pm 0.02) \mathrm{cm}\end{array}$
19
A thin copper wire of length $\ell$ metre increases in length by 2% when heated through $10 ^ { \circ } \mathrm { C }$. What is the percentage increase in area when a square copper sheet of length $\ell$ metre is heated through $10 ^ { \circ } \mathrm { C }$ ?
  1. A 4%
  2. B 8%
  3. C 16%
  4. D None of these
Show answer & explanation

Correct answer: A

$\mathrm{A}=\ell^{2} \Rightarrow \frac{\Delta \mathrm{~A}}{\mathrm{~A}} \times 100=2 \frac{\Delta \ell}{\ell} \times 100=2(2 \%)=4 \%$
20
The resistance is $R = \frac { V } { I }$ where $V = ( 100 \pm 5 )$ volt and $\mathrm { I } = ( 10 \pm 0.2 )$ ampere. What is the total error in R ?
  1. A 5%
  2. B 7%
  3. C 5.2%
  4. D $\left( \frac { 5 } { 2 } \right) \%$
Show answer & explanation

Correct answer: B

$\begin{array}{l}\mathrm{R}=\frac{\mathrm{V}}{\mathrm{I}} \Rightarrow \frac{\Delta \mathrm{R}}{\mathrm{R}}=\frac{\Delta \mathrm{V}}{\mathrm{V}}+\frac{\Delta \mathrm{I}}{\mathrm{I}} \\ \Rightarrow \frac{\Delta \mathrm{R}}{\mathrm{R}} \times 100=\left(\frac{5}{100} \times 100+\frac{0.2}{10} \times 100\right)=7 \%\end{array}$

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