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

 Page 1


1 . A and B have different dimensions. Then which of the
following relation will be meaningful ?
( a)
ú
û
ù
ê
ë
é
B
A
(b) [A – B ]
(c)[A + B] (d) [e
A/B
]
2 . N divisions on the main scale of a vernier calliper coincide
with (N + 1) divisions of the vernier scale. If each division of
main scale is ‘a’ units, then the least count of the instrument
is
( a) a (b)
a
N
(c)
1
N
a
N
´
+
(d)
1
a
N +
3 . Young’s modulus of a material has the same unit as
(a) pressure
(b) strain
(c) compressibility
(d) force
4 . The time period of a body under S.H.M. is represented by:
T = P
a
 D
b
 S
c
 where P is pressure, D is density and S is
surface tension, then values of a, b and c are
( a) 1 ,
2
1
,
2
3
- (b) 3 , 2 , 1 - -
(c)
2
1
,
2
3
,
2
1
- - (d) 1, 2, 
1
3
l a c i s y h P
 
d l r o W ,
 
s t i n U
 
&
 
s t n e m e r u s a e M
JEE	Main	Numericals
Page 2


1 . A and B have different dimensions. Then which of the
following relation will be meaningful ?
( a)
ú
û
ù
ê
ë
é
B
A
(b) [A – B ]
(c)[A + B] (d) [e
A/B
]
2 . N divisions on the main scale of a vernier calliper coincide
with (N + 1) divisions of the vernier scale. If each division of
main scale is ‘a’ units, then the least count of the instrument
is
( a) a (b)
a
N
(c)
1
N
a
N
´
+
(d)
1
a
N +
3 . Young’s modulus of a material has the same unit as
(a) pressure
(b) strain
(c) compressibility
(d) force
4 . The time period of a body under S.H.M. is represented by:
T = P
a
 D
b
 S
c
 where P is pressure, D is density and S is
surface tension, then values of a, b and c are
( a) 1 ,
2
1
,
2
3
- (b) 3 , 2 , 1 - -
(c)
2
1
,
2
3
,
2
1
- - (d) 1, 2, 
1
3
l a c i s y h P
 
d l r o W ,
 
s t i n U
 
&
 
s t n e m e r u s a e M
JEE	Main	Numericals
5. In the eqn. 
2
a
P (V b) constant,
V
æö
+-=
ç÷
èø
 the unit of a is
(a) dyne cm
5
(b) dyne cm
4
(c) dyne/cm
3
(d) dyne cm
2
6. The mass and volume of a body are found to be 5.00 ± 0.05
kg and 1.00 ± 0.05 m
3
 respectively. Then the maximum
possible percentage error in its density is
(a) 6% (b) 3%
(c) 10% (d) 5%
7. The density of material in CGS system of units is 4g/cm
3
. In
a system of units in which unit of length is 10 cm and unit of
mass is 100 g, the value of density of material will be
(a) 0.4 unit (b) 40 unit
(c) 400 unit (d) 0.04 unit
8. Of the following quantities, which one has dimensions
different from the remaining three?
(a) Energy per unit volume
(b) Force per unit area
(c) Product of voltage and charge per unit volume
(d) Angular momentum
9. The percentage error in measuring M, L and T are 1%, 1.5%
and 3% respectively. Then the percentage error in measuring
the physical quantity with dimensions ML
–1
 T
–1
 is
(a) 1% (b) 3.5%
(c) 3% (d) 5.5%
10. The unit of permittivity of free space, e
o
 is
(a) coulomb
2
/(newton-metre)
2
(b) coulomb/newton-metre
(c) newton-meter
2
/coulomb
2
(d) coulomb
2
/newton-metre
2
11. If E, m, J and G  represent energy , mass, angular momentum
and gravitational constant respectively, then the
dimensional formula of EJ
2
/m
5
G
2
 is same as that of the
(a) angle (b) length
(c) mass (d) time
12. The current voltage relation of a diode is given by I =
(e
1000V/T
 – 1)mA, where the applied voltage V is in volts
and the temperature T is in degree kelvin. If a student makes
an error measuring ±0.01 V while measuring the current of 5
mA at 300 K, what will be the error in the value of current in
mA?
(a) 0.2 mA (b) 0.02 mA
(c) 0.5 mA (d) 0.05 mA
13. The unit of impulse is the same as that of
(a) energy (b) power
(c) momentum (d) velocity
14. A student measured the length of a rod as 3.50 cm. Which
instrument did he use to measure it?
(a) A meter scale
(b) A vernier calliper where the 10 divisions in vernier scale
matches with 9 divisions in main scale and main scale
has 10 divisions in 1 cm
(c) A screw gauge having 100 divisions in the circular scale
and pitch as 1 mm
(d) A screw gauge having 50 divisions in the circular scale
and pitch as 1 mm
15. Weber is the unit of
(a) magnetic susceptibility
(b) intensity of magnetisation
(c) magnetic flux
(d) magnetic permeability
16. An object is moving through the liquid. The viscous
damping force acting on it is proportional to the velocity.
Then dimensions of constant of proportionality are
(a) [ML
–1
T
–1
] (b) [ML T
–1
]
(c) [M
0
LT
–1
] (d) [ML
0
T
–1
]
Page 3


1 . A and B have different dimensions. Then which of the
following relation will be meaningful ?
( a)
ú
û
ù
ê
ë
é
B
A
(b) [A – B ]
(c)[A + B] (d) [e
A/B
]
2 . N divisions on the main scale of a vernier calliper coincide
with (N + 1) divisions of the vernier scale. If each division of
main scale is ‘a’ units, then the least count of the instrument
is
( a) a (b)
a
N
(c)
1
N
a
N
´
+
(d)
1
a
N +
3 . Young’s modulus of a material has the same unit as
(a) pressure
(b) strain
(c) compressibility
(d) force
4 . The time period of a body under S.H.M. is represented by:
T = P
a
 D
b
 S
c
 where P is pressure, D is density and S is
surface tension, then values of a, b and c are
( a) 1 ,
2
1
,
2
3
- (b) 3 , 2 , 1 - -
(c)
2
1
,
2
3
,
2
1
- - (d) 1, 2, 
1
3
l a c i s y h P
 
d l r o W ,
 
s t i n U
 
&
 
s t n e m e r u s a e M
JEE	Main	Numericals
5. In the eqn. 
2
a
P (V b) constant,
V
æö
+-=
ç÷
èø
 the unit of a is
(a) dyne cm
5
(b) dyne cm
4
(c) dyne/cm
3
(d) dyne cm
2
6. The mass and volume of a body are found to be 5.00 ± 0.05
kg and 1.00 ± 0.05 m
3
 respectively. Then the maximum
possible percentage error in its density is
(a) 6% (b) 3%
(c) 10% (d) 5%
7. The density of material in CGS system of units is 4g/cm
3
. In
a system of units in which unit of length is 10 cm and unit of
mass is 100 g, the value of density of material will be
(a) 0.4 unit (b) 40 unit
(c) 400 unit (d) 0.04 unit
8. Of the following quantities, which one has dimensions
different from the remaining three?
(a) Energy per unit volume
(b) Force per unit area
(c) Product of voltage and charge per unit volume
(d) Angular momentum
9. The percentage error in measuring M, L and T are 1%, 1.5%
and 3% respectively. Then the percentage error in measuring
the physical quantity with dimensions ML
–1
 T
–1
 is
(a) 1% (b) 3.5%
(c) 3% (d) 5.5%
10. The unit of permittivity of free space, e
o
 is
(a) coulomb
2
/(newton-metre)
2
(b) coulomb/newton-metre
(c) newton-meter
2
/coulomb
2
(d) coulomb
2
/newton-metre
2
11. If E, m, J and G  represent energy , mass, angular momentum
and gravitational constant respectively, then the
dimensional formula of EJ
2
/m
5
G
2
 is same as that of the
(a) angle (b) length
(c) mass (d) time
12. The current voltage relation of a diode is given by I =
(e
1000V/T
 – 1)mA, where the applied voltage V is in volts
and the temperature T is in degree kelvin. If a student makes
an error measuring ±0.01 V while measuring the current of 5
mA at 300 K, what will be the error in the value of current in
mA?
(a) 0.2 mA (b) 0.02 mA
(c) 0.5 mA (d) 0.05 mA
13. The unit of impulse is the same as that of
(a) energy (b) power
(c) momentum (d) velocity
14. A student measured the length of a rod as 3.50 cm. Which
instrument did he use to measure it?
(a) A meter scale
(b) A vernier calliper where the 10 divisions in vernier scale
matches with 9 divisions in main scale and main scale
has 10 divisions in 1 cm
(c) A screw gauge having 100 divisions in the circular scale
and pitch as 1 mm
(d) A screw gauge having 50 divisions in the circular scale
and pitch as 1 mm
15. Weber is the unit of
(a) magnetic susceptibility
(b) intensity of magnetisation
(c) magnetic flux
(d) magnetic permeability
16. An object is moving through the liquid. The viscous
damping force acting on it is proportional to the velocity.
Then dimensions of constant of proportionality are
(a) [ML
–1
T
–1
] (b) [ML T
–1
]
(c) [M
0
LT
–1
] (d) [ML
0
T
–1
]
17. Two full turns of the circular scale of a screw gauge cover a
distance of 1mm on its main scale. The total number of
divisions on the circular scale is 50. Further, it is found that
the screw gauge has a zero error of –0.03 mm. While
measuring the diameter of a thin wire, a student notes the
main scale reading of 3 mm and the number of circular scale
divisions in line with the main scale as 35. The diameter of
the wire is
(a) 3.32 mm (b) 3.73 mm
(c) 3.67 mm (d) 3.38 mm
18. The SI unit of electric flux is
(a) Cm
–2
(b) coulomb
(c) ampere (d) volt metre
19. If Q denote the charge on the plate of a capacitor of
capacitance C then the dimensional formula for 
C
Q
2
 is
(a) [L
2
M
2
T] (b) [LMT
2
]
(c) [L
2
MT
–2
] (d) [L
2
M
2
T
2
]
20. The respective number of significant figures for the numbers
23.023, 0.0003 and 2.1 × 10
–3
 
are
(a) 5, 1, 2 (b) 5, 1, 5
(c) 5, 5, 2 (d) 4, 4, 2
21. The dimensions of mobility are
(a)M
–2
T
2
A (b) M
–1
T
2
A
(c)M
–2
T
3
A (d) M
–1
T
3
A
22. The physical quantities not having same dimensions are
(a) torque and work
(b) momentum and Planck’s constant
(c) stress and Young’s modulus
(d) speed and ( m
0
e
0
)
–1/2
23. In an experiment four quantities a, b, c and d are measured
with percentage error 1%, 2%, 3% and 4% respectively.
Quantity P is calculated as P = 
32
ab
cd
% error in P is
(a) 10% (b) 7%
(c) 4% (d) 14%
24. The density of a solid ball is to be determined in an
experiment. The diameter of the ball is measured with a screw
gauge, whose pitch is 0.5 mm and there are 50 divisions on
the circular scale. The reading on the main scale is
2.5 mm and that on the circular scale is 20 divisions. If the
measured mass of the ball has a relative error of 2%, the
relative percentage error in the density is
(a) 0.9% (b) 2.4%
(c) 3.1% (d) 4.2%
25. A quantity X is given by 
0
V
L
t
D
e
D
 where 
0
Î is the
permittivity of the free space, L is a length, DV is a potential
difference and Dt is a time interval. The dimensional formula
for X is the same as that of
(a) resistance (b) charge
(c) voltage (d) current
26. ln a simple pendulum experiment, the maximum percentage
error in the measurement of length is 2% and that in the
observation of the time-period is 3%. Then the maximum
percentage error in determination of the acceleration due to
gravity g is
(a) 5% (b) 6%
(c) 1% (d) 8%
Page 4


1 . A and B have different dimensions. Then which of the
following relation will be meaningful ?
( a)
ú
û
ù
ê
ë
é
B
A
(b) [A – B ]
(c)[A + B] (d) [e
A/B
]
2 . N divisions on the main scale of a vernier calliper coincide
with (N + 1) divisions of the vernier scale. If each division of
main scale is ‘a’ units, then the least count of the instrument
is
( a) a (b)
a
N
(c)
1
N
a
N
´
+
(d)
1
a
N +
3 . Young’s modulus of a material has the same unit as
(a) pressure
(b) strain
(c) compressibility
(d) force
4 . The time period of a body under S.H.M. is represented by:
T = P
a
 D
b
 S
c
 where P is pressure, D is density and S is
surface tension, then values of a, b and c are
( a) 1 ,
2
1
,
2
3
- (b) 3 , 2 , 1 - -
(c)
2
1
,
2
3
,
2
1
- - (d) 1, 2, 
1
3
l a c i s y h P
 
d l r o W ,
 
s t i n U
 
&
 
s t n e m e r u s a e M
JEE	Main	Numericals
5. In the eqn. 
2
a
P (V b) constant,
V
æö
+-=
ç÷
èø
 the unit of a is
(a) dyne cm
5
(b) dyne cm
4
(c) dyne/cm
3
(d) dyne cm
2
6. The mass and volume of a body are found to be 5.00 ± 0.05
kg and 1.00 ± 0.05 m
3
 respectively. Then the maximum
possible percentage error in its density is
(a) 6% (b) 3%
(c) 10% (d) 5%
7. The density of material in CGS system of units is 4g/cm
3
. In
a system of units in which unit of length is 10 cm and unit of
mass is 100 g, the value of density of material will be
(a) 0.4 unit (b) 40 unit
(c) 400 unit (d) 0.04 unit
8. Of the following quantities, which one has dimensions
different from the remaining three?
(a) Energy per unit volume
(b) Force per unit area
(c) Product of voltage and charge per unit volume
(d) Angular momentum
9. The percentage error in measuring M, L and T are 1%, 1.5%
and 3% respectively. Then the percentage error in measuring
the physical quantity with dimensions ML
–1
 T
–1
 is
(a) 1% (b) 3.5%
(c) 3% (d) 5.5%
10. The unit of permittivity of free space, e
o
 is
(a) coulomb
2
/(newton-metre)
2
(b) coulomb/newton-metre
(c) newton-meter
2
/coulomb
2
(d) coulomb
2
/newton-metre
2
11. If E, m, J and G  represent energy , mass, angular momentum
and gravitational constant respectively, then the
dimensional formula of EJ
2
/m
5
G
2
 is same as that of the
(a) angle (b) length
(c) mass (d) time
12. The current voltage relation of a diode is given by I =
(e
1000V/T
 – 1)mA, where the applied voltage V is in volts
and the temperature T is in degree kelvin. If a student makes
an error measuring ±0.01 V while measuring the current of 5
mA at 300 K, what will be the error in the value of current in
mA?
(a) 0.2 mA (b) 0.02 mA
(c) 0.5 mA (d) 0.05 mA
13. The unit of impulse is the same as that of
(a) energy (b) power
(c) momentum (d) velocity
14. A student measured the length of a rod as 3.50 cm. Which
instrument did he use to measure it?
(a) A meter scale
(b) A vernier calliper where the 10 divisions in vernier scale
matches with 9 divisions in main scale and main scale
has 10 divisions in 1 cm
(c) A screw gauge having 100 divisions in the circular scale
and pitch as 1 mm
(d) A screw gauge having 50 divisions in the circular scale
and pitch as 1 mm
15. Weber is the unit of
(a) magnetic susceptibility
(b) intensity of magnetisation
(c) magnetic flux
(d) magnetic permeability
16. An object is moving through the liquid. The viscous
damping force acting on it is proportional to the velocity.
Then dimensions of constant of proportionality are
(a) [ML
–1
T
–1
] (b) [ML T
–1
]
(c) [M
0
LT
–1
] (d) [ML
0
T
–1
]
17. Two full turns of the circular scale of a screw gauge cover a
distance of 1mm on its main scale. The total number of
divisions on the circular scale is 50. Further, it is found that
the screw gauge has a zero error of –0.03 mm. While
measuring the diameter of a thin wire, a student notes the
main scale reading of 3 mm and the number of circular scale
divisions in line with the main scale as 35. The diameter of
the wire is
(a) 3.32 mm (b) 3.73 mm
(c) 3.67 mm (d) 3.38 mm
18. The SI unit of electric flux is
(a) Cm
–2
(b) coulomb
(c) ampere (d) volt metre
19. If Q denote the charge on the plate of a capacitor of
capacitance C then the dimensional formula for 
C
Q
2
 is
(a) [L
2
M
2
T] (b) [LMT
2
]
(c) [L
2
MT
–2
] (d) [L
2
M
2
T
2
]
20. The respective number of significant figures for the numbers
23.023, 0.0003 and 2.1 × 10
–3
 
are
(a) 5, 1, 2 (b) 5, 1, 5
(c) 5, 5, 2 (d) 4, 4, 2
21. The dimensions of mobility are
(a)M
–2
T
2
A (b) M
–1
T
2
A
(c)M
–2
T
3
A (d) M
–1
T
3
A
22. The physical quantities not having same dimensions are
(a) torque and work
(b) momentum and Planck’s constant
(c) stress and Young’s modulus
(d) speed and ( m
0
e
0
)
–1/2
23. In an experiment four quantities a, b, c and d are measured
with percentage error 1%, 2%, 3% and 4% respectively.
Quantity P is calculated as P = 
32
ab
cd
% error in P is
(a) 10% (b) 7%
(c) 4% (d) 14%
24. The density of a solid ball is to be determined in an
experiment. The diameter of the ball is measured with a screw
gauge, whose pitch is 0.5 mm and there are 50 divisions on
the circular scale. The reading on the main scale is
2.5 mm and that on the circular scale is 20 divisions. If the
measured mass of the ball has a relative error of 2%, the
relative percentage error in the density is
(a) 0.9% (b) 2.4%
(c) 3.1% (d) 4.2%
25. A quantity X is given by 
0
V
L
t
D
e
D
 where 
0
Î is the
permittivity of the free space, L is a length, DV is a potential
difference and Dt is a time interval. The dimensional formula
for X is the same as that of
(a) resistance (b) charge
(c) voltage (d) current
26. ln a simple pendulum experiment, the maximum percentage
error in the measurement of length is 2% and that in the
observation of the time-period is 3%. Then the maximum
percentage error in determination of the acceleration due to
gravity g is
(a) 5% (b) 6%
(c) 1% (d) 8%
27. The dimensions of 
hc
e 1
2
o
Î
 are
( a) M
–1
 L
–3
 T
4
 A
2
(b) ML
3 
 T
–4
 A
–2
(c)M
0
 L
0
 T
0
 A
0
(d) M
–1
 L
–3
 T
2
 A
28. If the capacitance of a nanocapacitor is measured in terms
of a unit ‘u’ made by combining the electric charge ‘e’,
Bohr radius ‘a
0
’, Planck’s constant ‘h’ and speed of light ‘c’
then
( a)
2
0
eh
u
a
=
(b) 2
0
hc
u
ea
=
(c)
2
0
ec
u
h a
=
(d)
2
0
ea
u
hc
=
29. In an experiment the angles are required to be measured
using an instrument, 29 divisions of the main scale exactly
coincide with the 30 divisions of the vernier scale. If the
smallest division of the main scale is half- a degree (= 0.5°),
then the least count of the instrument is :
(a) half minute (b) one degree
(c) half degree (d) one minute
30. A physical quantity of the dimensions of length that can be
formed out of c, G and 
2
0
e
4pe
is [c is velocity of light, G is
universal constant of gravitation and e is charge]
( a)
1/2
2
2
0
e
cG
4
éù
êú
pe
êú
ëû
(b)
1/2
2
2
0
1e
G4
c
éù
êú
pe
êú
ëû
(c)
2
0
1e
G
c4pe
(d)
1/2
2
2
0
1e
G
4
c
éù
êú
pe
êú
ëû
Page 5


1 . A and B have different dimensions. Then which of the
following relation will be meaningful ?
( a)
ú
û
ù
ê
ë
é
B
A
(b) [A – B ]
(c)[A + B] (d) [e
A/B
]
2 . N divisions on the main scale of a vernier calliper coincide
with (N + 1) divisions of the vernier scale. If each division of
main scale is ‘a’ units, then the least count of the instrument
is
( a) a (b)
a
N
(c)
1
N
a
N
´
+
(d)
1
a
N +
3 . Young’s modulus of a material has the same unit as
(a) pressure
(b) strain
(c) compressibility
(d) force
4 . The time period of a body under S.H.M. is represented by:
T = P
a
 D
b
 S
c
 where P is pressure, D is density and S is
surface tension, then values of a, b and c are
( a) 1 ,
2
1
,
2
3
- (b) 3 , 2 , 1 - -
(c)
2
1
,
2
3
,
2
1
- - (d) 1, 2, 
1
3
l a c i s y h P
 
d l r o W ,
 
s t i n U
 
&
 
s t n e m e r u s a e M
JEE	Main	Numericals
5. In the eqn. 
2
a
P (V b) constant,
V
æö
+-=
ç÷
èø
 the unit of a is
(a) dyne cm
5
(b) dyne cm
4
(c) dyne/cm
3
(d) dyne cm
2
6. The mass and volume of a body are found to be 5.00 ± 0.05
kg and 1.00 ± 0.05 m
3
 respectively. Then the maximum
possible percentage error in its density is
(a) 6% (b) 3%
(c) 10% (d) 5%
7. The density of material in CGS system of units is 4g/cm
3
. In
a system of units in which unit of length is 10 cm and unit of
mass is 100 g, the value of density of material will be
(a) 0.4 unit (b) 40 unit
(c) 400 unit (d) 0.04 unit
8. Of the following quantities, which one has dimensions
different from the remaining three?
(a) Energy per unit volume
(b) Force per unit area
(c) Product of voltage and charge per unit volume
(d) Angular momentum
9. The percentage error in measuring M, L and T are 1%, 1.5%
and 3% respectively. Then the percentage error in measuring
the physical quantity with dimensions ML
–1
 T
–1
 is
(a) 1% (b) 3.5%
(c) 3% (d) 5.5%
10. The unit of permittivity of free space, e
o
 is
(a) coulomb
2
/(newton-metre)
2
(b) coulomb/newton-metre
(c) newton-meter
2
/coulomb
2
(d) coulomb
2
/newton-metre
2
11. If E, m, J and G  represent energy , mass, angular momentum
and gravitational constant respectively, then the
dimensional formula of EJ
2
/m
5
G
2
 is same as that of the
(a) angle (b) length
(c) mass (d) time
12. The current voltage relation of a diode is given by I =
(e
1000V/T
 – 1)mA, where the applied voltage V is in volts
and the temperature T is in degree kelvin. If a student makes
an error measuring ±0.01 V while measuring the current of 5
mA at 300 K, what will be the error in the value of current in
mA?
(a) 0.2 mA (b) 0.02 mA
(c) 0.5 mA (d) 0.05 mA
13. The unit of impulse is the same as that of
(a) energy (b) power
(c) momentum (d) velocity
14. A student measured the length of a rod as 3.50 cm. Which
instrument did he use to measure it?
(a) A meter scale
(b) A vernier calliper where the 10 divisions in vernier scale
matches with 9 divisions in main scale and main scale
has 10 divisions in 1 cm
(c) A screw gauge having 100 divisions in the circular scale
and pitch as 1 mm
(d) A screw gauge having 50 divisions in the circular scale
and pitch as 1 mm
15. Weber is the unit of
(a) magnetic susceptibility
(b) intensity of magnetisation
(c) magnetic flux
(d) magnetic permeability
16. An object is moving through the liquid. The viscous
damping force acting on it is proportional to the velocity.
Then dimensions of constant of proportionality are
(a) [ML
–1
T
–1
] (b) [ML T
–1
]
(c) [M
0
LT
–1
] (d) [ML
0
T
–1
]
17. Two full turns of the circular scale of a screw gauge cover a
distance of 1mm on its main scale. The total number of
divisions on the circular scale is 50. Further, it is found that
the screw gauge has a zero error of –0.03 mm. While
measuring the diameter of a thin wire, a student notes the
main scale reading of 3 mm and the number of circular scale
divisions in line with the main scale as 35. The diameter of
the wire is
(a) 3.32 mm (b) 3.73 mm
(c) 3.67 mm (d) 3.38 mm
18. The SI unit of electric flux is
(a) Cm
–2
(b) coulomb
(c) ampere (d) volt metre
19. If Q denote the charge on the plate of a capacitor of
capacitance C then the dimensional formula for 
C
Q
2
 is
(a) [L
2
M
2
T] (b) [LMT
2
]
(c) [L
2
MT
–2
] (d) [L
2
M
2
T
2
]
20. The respective number of significant figures for the numbers
23.023, 0.0003 and 2.1 × 10
–3
 
are
(a) 5, 1, 2 (b) 5, 1, 5
(c) 5, 5, 2 (d) 4, 4, 2
21. The dimensions of mobility are
(a)M
–2
T
2
A (b) M
–1
T
2
A
(c)M
–2
T
3
A (d) M
–1
T
3
A
22. The physical quantities not having same dimensions are
(a) torque and work
(b) momentum and Planck’s constant
(c) stress and Young’s modulus
(d) speed and ( m
0
e
0
)
–1/2
23. In an experiment four quantities a, b, c and d are measured
with percentage error 1%, 2%, 3% and 4% respectively.
Quantity P is calculated as P = 
32
ab
cd
% error in P is
(a) 10% (b) 7%
(c) 4% (d) 14%
24. The density of a solid ball is to be determined in an
experiment. The diameter of the ball is measured with a screw
gauge, whose pitch is 0.5 mm and there are 50 divisions on
the circular scale. The reading on the main scale is
2.5 mm and that on the circular scale is 20 divisions. If the
measured mass of the ball has a relative error of 2%, the
relative percentage error in the density is
(a) 0.9% (b) 2.4%
(c) 3.1% (d) 4.2%
25. A quantity X is given by 
0
V
L
t
D
e
D
 where 
0
Î is the
permittivity of the free space, L is a length, DV is a potential
difference and Dt is a time interval. The dimensional formula
for X is the same as that of
(a) resistance (b) charge
(c) voltage (d) current
26. ln a simple pendulum experiment, the maximum percentage
error in the measurement of length is 2% and that in the
observation of the time-period is 3%. Then the maximum
percentage error in determination of the acceleration due to
gravity g is
(a) 5% (b) 6%
(c) 1% (d) 8%
27. The dimensions of 
hc
e 1
2
o
Î
 are
( a) M
–1
 L
–3
 T
4
 A
2
(b) ML
3 
 T
–4
 A
–2
(c)M
0
 L
0
 T
0
 A
0
(d) M
–1
 L
–3
 T
2
 A
28. If the capacitance of a nanocapacitor is measured in terms
of a unit ‘u’ made by combining the electric charge ‘e’,
Bohr radius ‘a
0
’, Planck’s constant ‘h’ and speed of light ‘c’
then
( a)
2
0
eh
u
a
=
(b) 2
0
hc
u
ea
=
(c)
2
0
ec
u
h a
=
(d)
2
0
ea
u
hc
=
29. In an experiment the angles are required to be measured
using an instrument, 29 divisions of the main scale exactly
coincide with the 30 divisions of the vernier scale. If the
smallest division of the main scale is half- a degree (= 0.5°),
then the least count of the instrument is :
(a) half minute (b) one degree
(c) half degree (d) one minute
30. A physical quantity of the dimensions of length that can be
formed out of c, G and 
2
0
e
4pe
is [c is velocity of light, G is
universal constant of gravitation and e is charge]
( a)
1/2
2
2
0
e
cG
4
éù
êú
pe
êú
ëû
(b)
1/2
2
2
0
1e
G4
c
éù
êú
pe
êú
ëû
(c)
2
0
1e
G
c4pe
(d)
1/2
2
2
0
1e
G
4
c
éù
êú
pe
êú
ëû
1 . ( a ) A and B have different dimensions. Hence, only A and
B in a ratio form and is meaningful.
2. (d) No of divisions on main scale = N
No of divisions on vernier scale = N + 1
size of main scale division = a
Let size of vernier scale division be b
then we have
aN = b (N + 1) Þ b = 
1
aN
N+
Least count is a – b = a – 
1
aN
N+
= 
1
1
NN
a
N
+-éù
êú
+
ëû
 = 
1
a
N +
3 . ( a )
Stress Force / Area
Y Y Pressure.
Strain Dimensionless
== Þ=
4 . ( a ) T = P
a
 D
b
 S
c
M
0
L
0
T
1
 = (ML
–1
 T
–2
)
a
 (ML
–3
)
b
 (MT
–2
)
c
= M
a+b+c
 L
–a–3b
 T
–2a–2c
Applying principle of homogeneity
a + b + c = 0;  – a – 3b = 0;  – 2a – 2c = 1
on solving, we get a = – 3/2, b = 1/2, c = 1
5. (b) As 
P
V
a
2
=
2
a PV\= 
324
2
dyne
(cm ) dyne cm
cm
==
6 . ( a ) Here, Mass of a body , M = 5.00 ± 0.05 kg
V olume of a body , V = 1.00 ± 0.05 m
3
Density, r = 
M
V
Relative error in density is,  
MV
MV
DrDD
=+
r
Percentage error in density is
MV
100 100 100
MV
DrDD
´=´+´
r
0.05 0.05
100 100
51
æ öæ ö
=´+´
ç ÷ç ÷
è øè ø
 = 1% + 5% = 6%
7. (b) In CGS system,
3
g
4
cm
d =
The unit of mass is 100g and unit of length is 10 cm, so
density = 
3
100g
4
100
10
cm
10
æö
ç÷
èø
æö
ç÷
èø
= 
33
4
(100g) 10 0
(10cm)
1
10
æö
ç÷
èø
æö
ç÷
èø
3
3
4 100g
(10) ·
100
(10cm)
=´
= 40 unit
8. (d) For angular momentum, the dimensional formula is
[ML
2
T
–1
]. For other three, it is [ML
2
T
–2
] .
9. (d) Let X = ML
–1
 T
–1
Then,  
XMLT
100 100
XMLT
DDDDæö
´=++´
ç÷
èø
As we know,  
MLT
1%, 1.5% and 3%
MLT
DDD
===
= (1 + 1.5 + 3) % = 5.5 %.
10. (d)
F 4 ) r (
q
2
2
o
p
= e
Þ unit of e
o
 is (coulomb)
2
/ newton-metre
2
11. (a) ] T L M [
] T L M ][ M [
] T ML ][ T ML [
0 0 0
2 2 3 1 5
2 12 22
=
- -
- -
 = angle.
12. (a) The current voltage relation of diode is
I = (e
1000 V/T
 – 1) mA (given)
When, I = 5 mA, e
1000 V/T
 = 6mA
Also, 
1000 /
1000
()=´
VT
dIe
T
(By exponential function)
= 
1000
(6 ) (0.01)
300
´´ mA = 0.2 mA
13. (c) Impulse = change in momentum
14. (b) Measured length of rod = 3.50 cm
For vernier scale with 1 Main Scale Division = 1 mm
9 Main Scale Division = 10 Vernier Scale Division,
Least count = 1 MSD –1 VSD = 0.1 mm
15. (c) Weber is the unit of magnetic flux in S.I. system.
1 Wb(S.I unit) = 10
8
 maxwell
16. (d)
2
01
1
[][]
-
-
-
éù
éù
µÞ=Þ===
êú
êú
ëû
êú
ëû
F MLT
F v F kv k MLT
v
LT
17. (d) Least count of screw gauge = 
0.5
mm 0.01mm
50
=
\ Reading = [Main scale reading  + circular scale
                            reading × L.C] – (zero error)
= [3 + 35 × 0.01] – (–0.03) = 3.38 mm
HINTS & SOLUTIONS