Physical World, Units & Measurements Practice Questions - DPP for JEE

 Page 1


PART-I (Single Correct MCQs)
1. A and B have different dimensions. Then which of the following
relation will be meaningful ?
(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)
(c)
Page 2


PART-I (Single Correct MCQs)
1. A and B have different dimensions. Then which of the following
relation will be meaningful ?
(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)
(c)
(d)
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)
(b)
(c)
(d) 1, 2, 
5. In the eqn.  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. Of the following quantities, which one has dimensions different from
Page 3


PART-I (Single Correct MCQs)
1. A and B have different dimensions. Then which of the following
relation will be meaningful ?
(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)
(c)
(d)
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)
(b)
(c)
(d) 1, 2, 
5. In the eqn.  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. 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
8. 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%
9. 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)
(b)
(c)
(d)
10. 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
Page 4


PART-I (Single Correct MCQs)
1. A and B have different dimensions. Then which of the following
relation will be meaningful ?
(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)
(c)
(d)
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)
(b)
(c)
(d) 1, 2, 
5. In the eqn.  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. 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
8. 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%
9. 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)
(b)
(c)
(d)
10. 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
11. A quantity X is given by  where  is the permittivity of the
free space, L is a length, ?V is a potential difference and ?t is a time
interval. The dimensional formula for X is the same as that of
(a) resistance
(b) charge
(c) voltage
(d) current
12. 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 = % error in P is
(a) 10%
(b) 7%
(c) 4%
(d) 14%
13. If Q denote the charge on the plate of a capacitor of capacitance C then
the dimensional formula for  is
(a) [L
2
M
2
T]
(b) [LMT
2
]
(c) [L
2
MT
–2
]
(d) [L
2
M
2
T
2
]
14. 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
15. The dimensions of mobility are
Page 5


PART-I (Single Correct MCQs)
1. A and B have different dimensions. Then which of the following
relation will be meaningful ?
(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)
(c)
(d)
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)
(b)
(c)
(d) 1, 2, 
5. In the eqn.  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. 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
8. 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%
9. 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)
(b)
(c)
(d)
10. 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
11. A quantity X is given by  where  is the permittivity of the
free space, L is a length, ?V is a potential difference and ?t is a time
interval. The dimensional formula for X is the same as that of
(a) resistance
(b) charge
(c) voltage
(d) current
12. 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 = % error in P is
(a) 10%
(b) 7%
(c) 4%
(d) 14%
13. If Q denote the charge on the plate of a capacitor of capacitance C then
the dimensional formula for  is
(a) [L
2
M
2
T]
(b) [LMT
2
]
(c) [L
2
MT
–2
]
(d) [L
2
M
2
T
2
]
14. 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
15. 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
16. 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 (µ
0
e
0
)
–1/2
17. 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
18. The unit of impulse is the same as that of
(a) energy
(b) power
(c) momentum
(d) velocity
19. 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) [MLT
–1
]
(c) [M
0
LT
–1
]