Solutions Slot – 1 (Physics) Page # 1
UNITS & DIMENSIONS
EXERCISE – I SINGLE CORRECT
1 Fundamental quantities does not depends each
other PV
R= T → Temperature
So, In length, time and velocity here velocity nT
is derived quantities.
N / m2 × m3
2 Kilogram is not a physical quantity, its a unit. = R → Univ. Gas. Const.
mol. × K
n → No. of male
3 Light year is a unit of distance, which is cover
by light in a year. N−m
= = Joule K −1mol−1
mol. × K
4 PARSEC is a unit of distance. 9 Unit of impulse = V sec.
It is used in astronmiccal science.
m
= kg sec
sec2
5 Salar day → Time far Earth to wake a complete
rotation on its axis m
= kg
Parallactic second [1 Parsec] → It is a distance sec
corresponding to a parallex of one second of The unit is same as the unit of linear momentum.
arc.
10 Energy W = f × d = Nm
Leap year → A leap year is year (time) Containing
W = eV = electron-volt
one extra day.
W = p × t = Watt hour
Lunar Month → A lunar month is the time
So, kg × m/sec2 is not the unit of energy.
between two identical view moons of full moons.
11 We know n, u, = n2u2
1 Lunar month = 29.53059 days. when n1 > n2 when n1 < n2
6 System is NOT based on unit of mass, length or
and time alone, then u1 < u2 then u1 > u2
This system is based on all 7 Fundamental Ex. 1 m = 100 cm
physical quantities and 2 supplymentary physical Here 1 < 100
quantities. m > cm
1
7 SI unit of universal gravitational constant G So, we can say n ×
u
is -
GM1M2 12. Unit of length is micrometer
We know F = Unit of time is mirosecond
R2
Here M1 and M2 are mass Displacement
∵ Velocity
y =
R = Distance between them Time tan ker
F = Force 10 −6 m
= = m / sec
FR 2 N − m2 10−6 sec
G= =
M1M2 kg2 W
13 P=
t
So, Unit of G = N–m2 kg–2 Watt = Joule/sec.
Joule = Watt-sec.
2 Unit of universal gas constant (R) One watt-hour = 1 watt×60×60 sec
PV = nRT P → Pressure = 3600 watt-sec
V → Volume = 3600 Joule
= 3.6 × 103 Joule
394 - Rajeev Gandhi Nagar Kota, Ph. No. 0744-2209671, 93141-87482, 93527-21564
IVRS No. 0744-2439051, 0744-2439052, 0744-2439053 www.motioniitjee.com,
, Page # 2 Solutions Slot – 1 (Physics)
Displacement M1L2 T −2
14 Force × Dimension = = M1L2T-2K-1
Time K1
1 1 −2 L1 24 Plank Const. (h) →
= mLT × = M1L2 T −3
T1 Unit → J-S
So, Dimension of length here is 2. Dimension = M1L 2T-2 × T1
= M1L2T-1
This is also a dimension of Angular momentum.
1
15 Angular Frequency (f) = = MoLo T −1
T
Dimension of c
So, here dimension in length is zero
[t] = [c]
[c] = T1
16 Dimensionless quantity may have a unit
Dimension of b
Ex. Angle Unit → Radian
Dimension → MoLoTo b
[v] = t + c
17 A unitless quantity never has a nonzero
dimension or unit less quantity never has a
dimension b
25 v = at +
t+c
Change in length
Ex. Strain = Same physical quantity can be added or
Original length
substracted.
It has no unit and dimension → MoLoTo Dimension of a
[v] = [at]
18 Only same physical quantities can be added
or substracted, [v] L1 T −1
[a] = = 1
= L1T −2
It’s only multiply and divided only. [t] T
So, a/b denote a new physical quantity. Here t + c is also a Time (t)
b
19 They Can’t e added or Substracted in Same [v] =
t
expression.
[b] = [v] [t] = L1T-1 × T1
[b] = L1
20 (A, B, C) vo
26 x(t) = [1 − e− αt ]
α
21 (A) Dimension of vo and α
Here e–αt is dimensionless so,
21 Dimension of universal gravitational const. [α] [t] = MoLoTo
G M1M2 MoLo T o
F= [α] = = T −1
R2 T1
FR 2 M1L1 T −2 × L2 [α] = MoLoT-1
G= = = M−1L3 T −2
M1M2 M2 Here 1-e–αt is a number
22 Stefan-Constant(σ) Vo
[x(t)] =
Unit → w/m2-k4 = wm-2k-4 α
[Vo] = [L1] [T–1]
23 Baltz mann’s const. (k) → [Vo] = MoL1T–1
Unit → J/k
27 P = Po Exp (–αt2)
Here Exp (–αt2) is a dimensionless
394 - Rajeev Gandhi Nagar Kota, Ph. No. 0744-2209671, 93141-87482, 93527-21564
IVRS No. 0744-2439051, 0744-2439052, 0744-2439053 www.motioniitjee.com,
UNITS & DIMENSIONS
EXERCISE – I SINGLE CORRECT
1 Fundamental quantities does not depends each
other PV
R= T → Temperature
So, In length, time and velocity here velocity nT
is derived quantities.
N / m2 × m3
2 Kilogram is not a physical quantity, its a unit. = R → Univ. Gas. Const.
mol. × K
n → No. of male
3 Light year is a unit of distance, which is cover
by light in a year. N−m
= = Joule K −1mol−1
mol. × K
4 PARSEC is a unit of distance. 9 Unit of impulse = V sec.
It is used in astronmiccal science.
m
= kg sec
sec2
5 Salar day → Time far Earth to wake a complete
rotation on its axis m
= kg
Parallactic second [1 Parsec] → It is a distance sec
corresponding to a parallex of one second of The unit is same as the unit of linear momentum.
arc.
10 Energy W = f × d = Nm
Leap year → A leap year is year (time) Containing
W = eV = electron-volt
one extra day.
W = p × t = Watt hour
Lunar Month → A lunar month is the time
So, kg × m/sec2 is not the unit of energy.
between two identical view moons of full moons.
11 We know n, u, = n2u2
1 Lunar month = 29.53059 days. when n1 > n2 when n1 < n2
6 System is NOT based on unit of mass, length or
and time alone, then u1 < u2 then u1 > u2
This system is based on all 7 Fundamental Ex. 1 m = 100 cm
physical quantities and 2 supplymentary physical Here 1 < 100
quantities. m > cm
1
7 SI unit of universal gravitational constant G So, we can say n ×
u
is -
GM1M2 12. Unit of length is micrometer
We know F = Unit of time is mirosecond
R2
Here M1 and M2 are mass Displacement
∵ Velocity
y =
R = Distance between them Time tan ker
F = Force 10 −6 m
= = m / sec
FR 2 N − m2 10−6 sec
G= =
M1M2 kg2 W
13 P=
t
So, Unit of G = N–m2 kg–2 Watt = Joule/sec.
Joule = Watt-sec.
2 Unit of universal gas constant (R) One watt-hour = 1 watt×60×60 sec
PV = nRT P → Pressure = 3600 watt-sec
V → Volume = 3600 Joule
= 3.6 × 103 Joule
394 - Rajeev Gandhi Nagar Kota, Ph. No. 0744-2209671, 93141-87482, 93527-21564
IVRS No. 0744-2439051, 0744-2439052, 0744-2439053 www.motioniitjee.com,
, Page # 2 Solutions Slot – 1 (Physics)
Displacement M1L2 T −2
14 Force × Dimension = = M1L2T-2K-1
Time K1
1 1 −2 L1 24 Plank Const. (h) →
= mLT × = M1L2 T −3
T1 Unit → J-S
So, Dimension of length here is 2. Dimension = M1L 2T-2 × T1
= M1L2T-1
This is also a dimension of Angular momentum.
1
15 Angular Frequency (f) = = MoLo T −1
T
Dimension of c
So, here dimension in length is zero
[t] = [c]
[c] = T1
16 Dimensionless quantity may have a unit
Dimension of b
Ex. Angle Unit → Radian
Dimension → MoLoTo b
[v] = t + c
17 A unitless quantity never has a nonzero
dimension or unit less quantity never has a
dimension b
25 v = at +
t+c
Change in length
Ex. Strain = Same physical quantity can be added or
Original length
substracted.
It has no unit and dimension → MoLoTo Dimension of a
[v] = [at]
18 Only same physical quantities can be added
or substracted, [v] L1 T −1
[a] = = 1
= L1T −2
It’s only multiply and divided only. [t] T
So, a/b denote a new physical quantity. Here t + c is also a Time (t)
b
19 They Can’t e added or Substracted in Same [v] =
t
expression.
[b] = [v] [t] = L1T-1 × T1
[b] = L1
20 (A, B, C) vo
26 x(t) = [1 − e− αt ]
α
21 (A) Dimension of vo and α
Here e–αt is dimensionless so,
21 Dimension of universal gravitational const. [α] [t] = MoLoTo
G M1M2 MoLo T o
F= [α] = = T −1
R2 T1
FR 2 M1L1 T −2 × L2 [α] = MoLoT-1
G= = = M−1L3 T −2
M1M2 M2 Here 1-e–αt is a number
22 Stefan-Constant(σ) Vo
[x(t)] =
Unit → w/m2-k4 = wm-2k-4 α
[Vo] = [L1] [T–1]
23 Baltz mann’s const. (k) → [Vo] = MoL1T–1
Unit → J/k
27 P = Po Exp (–αt2)
Here Exp (–αt2) is a dimensionless
394 - Rajeev Gandhi Nagar Kota, Ph. No. 0744-2209671, 93141-87482, 93527-21564
IVRS No. 0744-2439051, 0744-2439052, 0744-2439053 www.motioniitjee.com,
