Solved Example: Units & Measurements | Physics for JEE Main & Advanced PDF Download

 Page 1


JEE Solved Examples on Unit and Measurement 
JEE Mains 
Q1: The dimensional formula for Planck's constant is 
(A) [?? ?? ?? ?? -?? ] 
(B) [????
?? ?? ?? ] 
(C) [????
-?? ?? -?? ] 
(D) [?????? -?? ] 
Ans: (A) For the dimension formula for Plank's Constant, we need to know the relation ?? =
hc
?? Where 
E is the Energy 
?? is speed of light 
?? is the wave length 
 ?
?? · ?? ?? = h
 ? h =
[?? ?? 2
?? -2
][?? ]
[?? ?? -1
]
= [?? ?? 2
?? -1
]
 
 
 
Q2:  Turpentine oil is flowing through a tube of length ?? and radius ?? . The pressure difference 
between the two ends of the tube is ?? ; the viscosity of the oil is given by ?? =
?? (?? ?? -?? ?? )
?? ????
 where ?? is 
the velocity of oil at a distance ?? from the axis of the tube. From this relation, the dimensions of 
viscosity ?? are 
(A) [?? ?? ?? ?? ?? ?? ] 
(C) [????
?? ?? -?? ] 
(D) [????
-?? ?? -?? ] 
Ans: (D) ?? =
?? .(?? 2
-?? 2
)
4?? l
 
For the dimension of viscosity ?? =
 [pressure] [L
2
]
[LT
-1
][L]
 
We have to know the dimensions of pressure; which in turn is force per unit area. 
 ? [ pressure ] = [ML
-1
 T
-2
]
?? =
[ML
-1
 T
-2
][L
2
]
[?? T
-1
][L]
= [?? L
-1
 T
-1
]
 
 
 
 
 
Page 2


JEE Solved Examples on Unit and Measurement 
JEE Mains 
Q1: The dimensional formula for Planck's constant is 
(A) [?? ?? ?? ?? -?? ] 
(B) [????
?? ?? ?? ] 
(C) [????
-?? ?? -?? ] 
(D) [?????? -?? ] 
Ans: (A) For the dimension formula for Plank's Constant, we need to know the relation ?? =
hc
?? Where 
E is the Energy 
?? is speed of light 
?? is the wave length 
 ?
?? · ?? ?? = h
 ? h =
[?? ?? 2
?? -2
][?? ]
[?? ?? -1
]
= [?? ?? 2
?? -1
]
 
 
 
Q2:  Turpentine oil is flowing through a tube of length ?? and radius ?? . The pressure difference 
between the two ends of the tube is ?? ; the viscosity of the oil is given by ?? =
?? (?? ?? -?? ?? )
?? ????
 where ?? is 
the velocity of oil at a distance ?? from the axis of the tube. From this relation, the dimensions of 
viscosity ?? are 
(A) [?? ?? ?? ?? ?? ?? ] 
(C) [????
?? ?? -?? ] 
(D) [????
-?? ?? -?? ] 
Ans: (D) ?? =
?? .(?? 2
-?? 2
)
4?? l
 
For the dimension of viscosity ?? =
 [pressure] [L
2
]
[LT
-1
][L]
 
We have to know the dimensions of pressure; which in turn is force per unit area. 
 ? [ pressure ] = [ML
-1
 T
-2
]
?? =
[ML
-1
 T
-2
][L
2
]
[?? T
-1
][L]
= [?? L
-1
 T
-1
]
 
 
 
 
 
Q3:  The time dependence of a physical quantity is given by ?? = ?? ?? ?????? (-?? ?? ?? ) [Where ?? is a 
constant and ?? is time]. The constant ?? 
(A) Is dimensionless 
(B) Has dimensions [?? -?? ] 
(C) Has dimensions [?? ?? ] 
(D) Has dimensions of ?? 
Ans: (B) ?? = ?? 0
exp (-? ?? 2
) 
To find the constant ?; 
Hint :- All the question inside the exp ( ) will finally end up with dimension [M
0
 L
0
 T
0
 ]. 
So, 
 ? [?][T
2
] = [M
0
 L
0
 T
0
]
[?] = [M
0
 L
0
 T
-2
]
 
? The dimension are [M
0
 L
0
 T
-2
] or [T
-2
] which is option B. 
 
 
Q4:  which of the following quantities can be written in SI units in ???? ?? ?? ?? -?? ?? -?? 
(A) Resistance 
(B) Inductance 
(C) Capacitance 
(D) Magnetic flux 
Ans: (A) In this, we verity each option to match the given dimension. 
Capacitance: [M
-1
 L
-2
 T
4
 A
2
] 
Resistance: [ML
2
 T
-3
 A
-2
] 
Inductance: [ML
2
 T
-2
 A
-2
] 
Mag. Flux: [ML
2
 T
-2
 A
-1
] 
So, the answer is resistance. i.e option (A). 
Tip: - Don't get tensed up if you don't know these terms. You will learn them later. For time being, do 
remember them. 
Q5:  If ?? and ?? denote inductance and resistance respectively, then the dimensions of ?? /?? is 
(A) [?? ?? ?? ?? ?? ?? ] 
(B) [?? ?? ?? ?? ?? ] 
(C) [?? ?? ?? ?? ?? ?? ] 
(D) [?????? ?? ] 
Ans: (B) Using the dimension mentioned in the above question, 
We get [?? /?? ] = [?? 0
?? 0
?? ] 
Tip: - Once check the dimension of (?? *
?? )!! 
 
 
Page 3


JEE Solved Examples on Unit and Measurement 
JEE Mains 
Q1: The dimensional formula for Planck's constant is 
(A) [?? ?? ?? ?? -?? ] 
(B) [????
?? ?? ?? ] 
(C) [????
-?? ?? -?? ] 
(D) [?????? -?? ] 
Ans: (A) For the dimension formula for Plank's Constant, we need to know the relation ?? =
hc
?? Where 
E is the Energy 
?? is speed of light 
?? is the wave length 
 ?
?? · ?? ?? = h
 ? h =
[?? ?? 2
?? -2
][?? ]
[?? ?? -1
]
= [?? ?? 2
?? -1
]
 
 
 
Q2:  Turpentine oil is flowing through a tube of length ?? and radius ?? . The pressure difference 
between the two ends of the tube is ?? ; the viscosity of the oil is given by ?? =
?? (?? ?? -?? ?? )
?? ????
 where ?? is 
the velocity of oil at a distance ?? from the axis of the tube. From this relation, the dimensions of 
viscosity ?? are 
(A) [?? ?? ?? ?? ?? ?? ] 
(C) [????
?? ?? -?? ] 
(D) [????
-?? ?? -?? ] 
Ans: (D) ?? =
?? .(?? 2
-?? 2
)
4?? l
 
For the dimension of viscosity ?? =
 [pressure] [L
2
]
[LT
-1
][L]
 
We have to know the dimensions of pressure; which in turn is force per unit area. 
 ? [ pressure ] = [ML
-1
 T
-2
]
?? =
[ML
-1
 T
-2
][L
2
]
[?? T
-1
][L]
= [?? L
-1
 T
-1
]
 
 
 
 
 
Q3:  The time dependence of a physical quantity is given by ?? = ?? ?? ?????? (-?? ?? ?? ) [Where ?? is a 
constant and ?? is time]. The constant ?? 
(A) Is dimensionless 
(B) Has dimensions [?? -?? ] 
(C) Has dimensions [?? ?? ] 
(D) Has dimensions of ?? 
Ans: (B) ?? = ?? 0
exp (-? ?? 2
) 
To find the constant ?; 
Hint :- All the question inside the exp ( ) will finally end up with dimension [M
0
 L
0
 T
0
 ]. 
So, 
 ? [?][T
2
] = [M
0
 L
0
 T
0
]
[?] = [M
0
 L
0
 T
-2
]
 
? The dimension are [M
0
 L
0
 T
-2
] or [T
-2
] which is option B. 
 
 
Q4:  which of the following quantities can be written in SI units in ???? ?? ?? ?? -?? ?? -?? 
(A) Resistance 
(B) Inductance 
(C) Capacitance 
(D) Magnetic flux 
Ans: (A) In this, we verity each option to match the given dimension. 
Capacitance: [M
-1
 L
-2
 T
4
 A
2
] 
Resistance: [ML
2
 T
-3
 A
-2
] 
Inductance: [ML
2
 T
-2
 A
-2
] 
Mag. Flux: [ML
2
 T
-2
 A
-1
] 
So, the answer is resistance. i.e option (A). 
Tip: - Don't get tensed up if you don't know these terms. You will learn them later. For time being, do 
remember them. 
Q5:  If ?? and ?? denote inductance and resistance respectively, then the dimensions of ?? /?? is 
(A) [?? ?? ?? ?? ?? ?? ] 
(B) [?? ?? ?? ?? ?? ] 
(C) [?? ?? ?? ?? ?? ?? ] 
(D) [?????? ?? ] 
Ans: (B) Using the dimension mentioned in the above question, 
We get [?? /?? ] = [?? 0
?? 0
?? ] 
Tip: - Once check the dimension of (?? *
?? )!! 
 
 
 
 
Q6:  The dimensions of (
?? ?? ) ? ?? ?? 
( ?? ?? : permittivity of free space; ?? : electric field) is 
(A) ?????? -?? 
(B) ????
?? ?? -?? 
(C) ????
-?? ?? -?? 
(D) ????
?? ?? -?? 
Ans: (C) Physically the term 
1
2
? E
2
 equals the electric energy per unit volume. i.e Energy/Volume. 
?
[ML
2
 T
-2
]
[L
3
]
= [ML
-1
 T
-2
] 
 
 
Q7:  Which of the following measurements is most accurate? 
(A) ?? . ?????? ???? 
(B) ?? . ???? ???? 
(C) ???? . ???? ???? 
(D) ?? . ?? ???? 
Ans: (C) Writing down the significant figures of all the options. 
0.005 - 1
5.00 - 3
50.00 - 4
5.0 - 2
 
 
 
Q8:  When 97.52 is divided by 2.54 , the correct result is 
(A) 38.3937 
(B) 38.394 
(C) 38.39 
(D) 38.4 
Ans: (D) 
(97.52)
?
4
×
(2.54)
?
3
 
? The final answer should be with 3 Significant figure. 
By observing the options, we can see that option (D) satisfies this condition. 
 
 
 
Page 4


JEE Solved Examples on Unit and Measurement 
JEE Mains 
Q1: The dimensional formula for Planck's constant is 
(A) [?? ?? ?? ?? -?? ] 
(B) [????
?? ?? ?? ] 
(C) [????
-?? ?? -?? ] 
(D) [?????? -?? ] 
Ans: (A) For the dimension formula for Plank's Constant, we need to know the relation ?? =
hc
?? Where 
E is the Energy 
?? is speed of light 
?? is the wave length 
 ?
?? · ?? ?? = h
 ? h =
[?? ?? 2
?? -2
][?? ]
[?? ?? -1
]
= [?? ?? 2
?? -1
]
 
 
 
Q2:  Turpentine oil is flowing through a tube of length ?? and radius ?? . The pressure difference 
between the two ends of the tube is ?? ; the viscosity of the oil is given by ?? =
?? (?? ?? -?? ?? )
?? ????
 where ?? is 
the velocity of oil at a distance ?? from the axis of the tube. From this relation, the dimensions of 
viscosity ?? are 
(A) [?? ?? ?? ?? ?? ?? ] 
(C) [????
?? ?? -?? ] 
(D) [????
-?? ?? -?? ] 
Ans: (D) ?? =
?? .(?? 2
-?? 2
)
4?? l
 
For the dimension of viscosity ?? =
 [pressure] [L
2
]
[LT
-1
][L]
 
We have to know the dimensions of pressure; which in turn is force per unit area. 
 ? [ pressure ] = [ML
-1
 T
-2
]
?? =
[ML
-1
 T
-2
][L
2
]
[?? T
-1
][L]
= [?? L
-1
 T
-1
]
 
 
 
 
 
Q3:  The time dependence of a physical quantity is given by ?? = ?? ?? ?????? (-?? ?? ?? ) [Where ?? is a 
constant and ?? is time]. The constant ?? 
(A) Is dimensionless 
(B) Has dimensions [?? -?? ] 
(C) Has dimensions [?? ?? ] 
(D) Has dimensions of ?? 
Ans: (B) ?? = ?? 0
exp (-? ?? 2
) 
To find the constant ?; 
Hint :- All the question inside the exp ( ) will finally end up with dimension [M
0
 L
0
 T
0
 ]. 
So, 
 ? [?][T
2
] = [M
0
 L
0
 T
0
]
[?] = [M
0
 L
0
 T
-2
]
 
? The dimension are [M
0
 L
0
 T
-2
] or [T
-2
] which is option B. 
 
 
Q4:  which of the following quantities can be written in SI units in ???? ?? ?? ?? -?? ?? -?? 
(A) Resistance 
(B) Inductance 
(C) Capacitance 
(D) Magnetic flux 
Ans: (A) In this, we verity each option to match the given dimension. 
Capacitance: [M
-1
 L
-2
 T
4
 A
2
] 
Resistance: [ML
2
 T
-3
 A
-2
] 
Inductance: [ML
2
 T
-2
 A
-2
] 
Mag. Flux: [ML
2
 T
-2
 A
-1
] 
So, the answer is resistance. i.e option (A). 
Tip: - Don't get tensed up if you don't know these terms. You will learn them later. For time being, do 
remember them. 
Q5:  If ?? and ?? denote inductance and resistance respectively, then the dimensions of ?? /?? is 
(A) [?? ?? ?? ?? ?? ?? ] 
(B) [?? ?? ?? ?? ?? ] 
(C) [?? ?? ?? ?? ?? ?? ] 
(D) [?????? ?? ] 
Ans: (B) Using the dimension mentioned in the above question, 
We get [?? /?? ] = [?? 0
?? 0
?? ] 
Tip: - Once check the dimension of (?? *
?? )!! 
 
 
 
 
Q6:  The dimensions of (
?? ?? ) ? ?? ?? 
( ?? ?? : permittivity of free space; ?? : electric field) is 
(A) ?????? -?? 
(B) ????
?? ?? -?? 
(C) ????
-?? ?? -?? 
(D) ????
?? ?? -?? 
Ans: (C) Physically the term 
1
2
? E
2
 equals the electric energy per unit volume. i.e Energy/Volume. 
?
[ML
2
 T
-2
]
[L
3
]
= [ML
-1
 T
-2
] 
 
 
Q7:  Which of the following measurements is most accurate? 
(A) ?? . ?????? ???? 
(B) ?? . ???? ???? 
(C) ???? . ???? ???? 
(D) ?? . ?? ???? 
Ans: (C) Writing down the significant figures of all the options. 
0.005 - 1
5.00 - 3
50.00 - 4
5.0 - 2
 
 
 
Q8:  When 97.52 is divided by 2.54 , the correct result is 
(A) 38.3937 
(B) 38.394 
(C) 38.39 
(D) 38.4 
Ans: (D) 
(97.52)
?
4
×
(2.54)
?
3
 
? The final answer should be with 3 Significant figure. 
By observing the options, we can see that option (D) satisfies this condition. 
 
 
 
Q9:  The density of a cube is measured by measuring its mass and the length of its sides. If the 
maximum error in the measurement of mass and length are ?? % and ?? % respectively, then the 
maximum error in the measurement of density is 
(A) ?? % 
(B) ?? % 
(C) ?? % 
(D) ?? % 
 Ans: (A) density =
 mass 
 volume 
 ? ?? =
?? ?? 3
??? ?? = (
??? ?? ) + 3 (
??? ?? ) = 3 + 3(2) ? (
??? ?? ) = 9%
 
 
 
Q10:  A physical quantity is represented by ?? = ?? ?? ?? ?? ?? . If percentage error in the measurement of 
?? , ?? and ?? are ?? %, ?? % and ?? % respectively, then total percentage error is 
(A) (???? - ???? + ???? )% 
(B) (???? + ???? + ???? )% 
(C) (???? - ???? - ???? )% 
(D) none of the above 
Ans: (B) This is just a generalization of the previous question. 
?? = ?? ?? ?? b
T
-c
?x
x
= a · (
?m
m
) + b(
?L
L
) + c(
?T
T
)
(
?x
x
) = (a ? +?? b + ?? c)%
 P .S:- don't get confused with ± c.
 
 
 
Q11:  The volume of a sphere is ?? . ???? ????
?? . The volume of 25 such spheres taking into account the 
significant figures is 
(A) ?? . ???? × ????
?? ????
?? 
(B) ???? . ?? ????
?? 
(C) ???? ????
?? 
(D) ???? . ???? ????
?? 
Ans: (B) Here volume is an intrinsic property of each sphere. So, it will have the same number of 
significant digit even they are measured in bulk. 
? The final result should be having 3 significant digit. Just multiply 1.75 × 25 and then scale the 
result to 3 significant digits. 
 
Page 5


JEE Solved Examples on Unit and Measurement 
JEE Mains 
Q1: The dimensional formula for Planck's constant is 
(A) [?? ?? ?? ?? -?? ] 
(B) [????
?? ?? ?? ] 
(C) [????
-?? ?? -?? ] 
(D) [?????? -?? ] 
Ans: (A) For the dimension formula for Plank's Constant, we need to know the relation ?? =
hc
?? Where 
E is the Energy 
?? is speed of light 
?? is the wave length 
 ?
?? · ?? ?? = h
 ? h =
[?? ?? 2
?? -2
][?? ]
[?? ?? -1
]
= [?? ?? 2
?? -1
]
 
 
 
Q2:  Turpentine oil is flowing through a tube of length ?? and radius ?? . The pressure difference 
between the two ends of the tube is ?? ; the viscosity of the oil is given by ?? =
?? (?? ?? -?? ?? )
?? ????
 where ?? is 
the velocity of oil at a distance ?? from the axis of the tube. From this relation, the dimensions of 
viscosity ?? are 
(A) [?? ?? ?? ?? ?? ?? ] 
(C) [????
?? ?? -?? ] 
(D) [????
-?? ?? -?? ] 
Ans: (D) ?? =
?? .(?? 2
-?? 2
)
4?? l
 
For the dimension of viscosity ?? =
 [pressure] [L
2
]
[LT
-1
][L]
 
We have to know the dimensions of pressure; which in turn is force per unit area. 
 ? [ pressure ] = [ML
-1
 T
-2
]
?? =
[ML
-1
 T
-2
][L
2
]
[?? T
-1
][L]
= [?? L
-1
 T
-1
]
 
 
 
 
 
Q3:  The time dependence of a physical quantity is given by ?? = ?? ?? ?????? (-?? ?? ?? ) [Where ?? is a 
constant and ?? is time]. The constant ?? 
(A) Is dimensionless 
(B) Has dimensions [?? -?? ] 
(C) Has dimensions [?? ?? ] 
(D) Has dimensions of ?? 
Ans: (B) ?? = ?? 0
exp (-? ?? 2
) 
To find the constant ?; 
Hint :- All the question inside the exp ( ) will finally end up with dimension [M
0
 L
0
 T
0
 ]. 
So, 
 ? [?][T
2
] = [M
0
 L
0
 T
0
]
[?] = [M
0
 L
0
 T
-2
]
 
? The dimension are [M
0
 L
0
 T
-2
] or [T
-2
] which is option B. 
 
 
Q4:  which of the following quantities can be written in SI units in ???? ?? ?? ?? -?? ?? -?? 
(A) Resistance 
(B) Inductance 
(C) Capacitance 
(D) Magnetic flux 
Ans: (A) In this, we verity each option to match the given dimension. 
Capacitance: [M
-1
 L
-2
 T
4
 A
2
] 
Resistance: [ML
2
 T
-3
 A
-2
] 
Inductance: [ML
2
 T
-2
 A
-2
] 
Mag. Flux: [ML
2
 T
-2
 A
-1
] 
So, the answer is resistance. i.e option (A). 
Tip: - Don't get tensed up if you don't know these terms. You will learn them later. For time being, do 
remember them. 
Q5:  If ?? and ?? denote inductance and resistance respectively, then the dimensions of ?? /?? is 
(A) [?? ?? ?? ?? ?? ?? ] 
(B) [?? ?? ?? ?? ?? ] 
(C) [?? ?? ?? ?? ?? ?? ] 
(D) [?????? ?? ] 
Ans: (B) Using the dimension mentioned in the above question, 
We get [?? /?? ] = [?? 0
?? 0
?? ] 
Tip: - Once check the dimension of (?? *
?? )!! 
 
 
 
 
Q6:  The dimensions of (
?? ?? ) ? ?? ?? 
( ?? ?? : permittivity of free space; ?? : electric field) is 
(A) ?????? -?? 
(B) ????
?? ?? -?? 
(C) ????
-?? ?? -?? 
(D) ????
?? ?? -?? 
Ans: (C) Physically the term 
1
2
? E
2
 equals the electric energy per unit volume. i.e Energy/Volume. 
?
[ML
2
 T
-2
]
[L
3
]
= [ML
-1
 T
-2
] 
 
 
Q7:  Which of the following measurements is most accurate? 
(A) ?? . ?????? ???? 
(B) ?? . ???? ???? 
(C) ???? . ???? ???? 
(D) ?? . ?? ???? 
Ans: (C) Writing down the significant figures of all the options. 
0.005 - 1
5.00 - 3
50.00 - 4
5.0 - 2
 
 
 
Q8:  When 97.52 is divided by 2.54 , the correct result is 
(A) 38.3937 
(B) 38.394 
(C) 38.39 
(D) 38.4 
Ans: (D) 
(97.52)
?
4
×
(2.54)
?
3
 
? The final answer should be with 3 Significant figure. 
By observing the options, we can see that option (D) satisfies this condition. 
 
 
 
Q9:  The density of a cube is measured by measuring its mass and the length of its sides. If the 
maximum error in the measurement of mass and length are ?? % and ?? % respectively, then the 
maximum error in the measurement of density is 
(A) ?? % 
(B) ?? % 
(C) ?? % 
(D) ?? % 
 Ans: (A) density =
 mass 
 volume 
 ? ?? =
?? ?? 3
??? ?? = (
??? ?? ) + 3 (
??? ?? ) = 3 + 3(2) ? (
??? ?? ) = 9%
 
 
 
Q10:  A physical quantity is represented by ?? = ?? ?? ?? ?? ?? . If percentage error in the measurement of 
?? , ?? and ?? are ?? %, ?? % and ?? % respectively, then total percentage error is 
(A) (???? - ???? + ???? )% 
(B) (???? + ???? + ???? )% 
(C) (???? - ???? - ???? )% 
(D) none of the above 
Ans: (B) This is just a generalization of the previous question. 
?? = ?? ?? ?? b
T
-c
?x
x
= a · (
?m
m
) + b(
?L
L
) + c(
?T
T
)
(
?x
x
) = (a ? +?? b + ?? c)%
 P .S:- don't get confused with ± c.
 
 
 
Q11:  The volume of a sphere is ?? . ???? ????
?? . The volume of 25 such spheres taking into account the 
significant figures is 
(A) ?? . ???? × ????
?? ????
?? 
(B) ???? . ?? ????
?? 
(C) ???? ????
?? 
(D) ???? . ???? ????
?? 
Ans: (B) Here volume is an intrinsic property of each sphere. So, it will have the same number of 
significant digit even they are measured in bulk. 
? The final result should be having 3 significant digit. Just multiply 1.75 × 25 and then scale the 
result to 3 significant digits. 
 
 
Q12:  The measurement of radius of a sphere is (?? . ???? ± ?? %)???? . The percentage error in volume 
of the sphere is 
(A) (?????? ± ?? %) 
(B) (?????? ± ?? %) 
C) (?????? ± ?? %) 
(D) (?????? ± ?? %) 
 Ans: (A) ?? =
4
3
?? ?? 3
??? ?? = 3. (
??? ?? )
(
??? ?? ) = 3(2%) ?
??? ?? = 6%
 
 
Q13:  In the measurement of ?? from the formula ?? -
?? ?????? ?? ?? ?? ?? , the quantity which should be 
measured with the best care is 
(A) W 
(B) ?? 
(C) ?? 
(D) ?? 
Ans: (C) ?? =
2?????? ?? ?? 4
?? 
?n
n
= (
?w
w
) + (
?g
g
) + (
?L
L
) + 4 (
??? r
) + (
??? ?? ) 
Here a small error in ?? gets magnified by four times in the final result. So, it has to be measured with 
care. 
 
 
Q14:  When the number 6.03587 is rounded off to the second place of decimals, it becomes 
(A) 6.035 
(B) 6.04 
(C) 6.03 
(D) None 
Ans: (B) Refer theory