Tamanna
Chaudhary
, Units and Dimensions
1. In a vernier callipers, one main scale division is 𝑥 𝑐𝑚 and 𝑛 division of the vernier scale coincide with (𝑛 −
1) divisions of the main scale. The least count (in 𝑐𝑚) of the callipers is
𝑛−1 𝑛𝑥 𝑥 𝑥
a) @ A𝑥 b) c) d)
𝑛 (𝑛 − 1) 𝑛 (𝑛 − 1)
2. If the speed of light (𝑐), acceleration due to gravity (𝑔) and pressure (𝑝) are taken as the fundamental
quantities, then the dimension of gravitational constant is
a) 𝑐 ! 𝑔" 𝑝#! b) 𝑐 " 𝑔! 𝑝#$ c) 𝑐𝑔% 𝑝#! d) 𝑐 #$ 𝑔" 𝑝#$
3. Dimension of 𝑅 is
a) 𝑀𝐿! 𝑇 #$ b) 𝑀𝐿! 𝑇 #% 𝐴#! c) 𝑀𝐿#$ 𝑇 #! d) None of these
4. “Pascal-Second” has dimension of
a) Force b) Energy
c) Pressure d) Coefficient of viscosity
5. The unit of physical quantity obtained by the line integral of electric field is
a) NC#$ b) Vm#$ c) JC#$ d) C! N#$ m#!
6. The dimensions of electric potential are
a) [𝑀𝐿! 𝑇 #! 𝑄#$ ] b) [𝑀𝐿𝑇 #! 𝑄#$ ] c) [𝑀𝐿! 𝑇 #$ 𝑄] d) [𝑀𝐿! 𝑇 #! 𝑄]
7. &
The velocity 𝑣 (in 𝑐𝑚/𝑠𝑒𝑐) of a particle is given in terms of time 𝑡(in 𝑠𝑒𝑐) by the relation 𝑣 = 𝑎𝑡 + '() ; the
dimensions of 𝑎, 𝑏 and 𝑐 are
a) 𝑎 = 𝐿! , 𝑏 = 𝑇, 𝑐 = 𝐿𝑇 ! b) 𝑎 = 𝐿𝑇 ! , 𝑏 = 𝐿𝑇, 𝑐 = 𝐿
c) 𝑎 = 𝐿𝑇 ! , 𝑏 = 𝐿, 𝑐 = 𝑇 d) 𝑎 = 𝐿, 𝑏 = 𝐿𝑇, 𝑐 = 𝑇 !
8. A student measures the distance traversed in free fall of a body, initially at rest in each time. He uses this
data to estimate 𝑔, the acceleration due to gravity. If the maximum percentage errors in measurement of
the distance and the time are 𝑒$ and 𝑒! respectively, the percentage error in the estimation of 𝑔 is
a) 𝑒! − 𝑒$ b) 𝑒$ + 2𝑒! c) 𝑒$ + 𝑒! d) 𝑒$ − 2𝑒!
9. Which of the following is the smallest unit
a) 𝑀𝑖𝑙𝑙𝑖𝑚𝑒𝑡𝑟𝑒 b) 𝐴𝑛𝑔𝑠𝑡𝑟𝑜𝑚 c) 𝐹𝑒𝑟𝑚𝑖 d) 𝑀𝑒𝑡𝑟𝑒
10. Which relation is wrong
a) 1 𝑐𝑎𝑙𝑜𝑟𝑖𝑒 = 4.18 𝑗𝑜𝑢𝑙𝑒 b) 1 Å = 10#$" 𝑚
c) 1 𝑀𝑒𝑉 = 1.6 × 10#$% 𝑗𝑜𝑢𝑙𝑒 d) 1 𝑛𝑒𝑤𝑡𝑜𝑛 = 10#* 𝑑𝑦𝑛𝑒
+
11. The resistance 𝑅 = where 𝑉 = 100 ± 5 𝑣𝑜𝑙𝑡𝑠 and 𝑖 = 10 ± 0.2 𝑎𝑚𝑝𝑒𝑟𝑒𝑠. What is the total error in 𝑅
,
5
a) 5% b) 7% c) 5.2% d) %
2
12. A vernier calipers has 1 𝑚𝑚 marks on the main scale. It has 20 equal divisions on the Vernier scale which
match with 16 main scale divisions. For this Vernier callipers, the least count is
a) 0.02 𝑚𝑚 b) 0.05 𝑚𝑚 c) 0.1 𝑚𝑚 d) 0.2 𝑚𝑚
, 13. Given 𝑋 = (𝐺ℎ/𝑐 % )$/! , where 𝐺, ℎ and 𝑐 are gravitational constant, Planck’s constant and the velocity of
light respectively. Dimensions of 𝑋 are the same as those of
a) Mass b) Time c) Length d) Acceleration
14. Number of base SI unit is
a) 4 b) 7 c) 3 d) 5
15. The dimensions of permittivity 𝜀" are
a) 𝐴! 𝑇 ! 𝑀#$ 𝐿#% b) 𝐴! 𝑇 . 𝑀#$ 𝐿#% c) 𝐴#! 𝑇 #. 𝑀𝐿% d) 𝐴! 𝑇 #. 𝑀#$ 𝐿#%
16. Two full turns of the circular scale of a screw gauge cover 1 mm 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
17. If 𝑥 = 𝑎 − 𝑏, then the maximum percentage error in the measurement of 𝑥 will be
∆𝑎 + ∆𝑏 ∆𝑎 ∆𝑏
a) @ A × 100% b) @ − A × 100%
𝑎−𝑏 𝑎 𝑏
∆𝑎 ∆𝑏 ∆𝑎 ∆𝑏
c) @ + A × 100% d) @ − A × 100%
𝑎−𝑎 𝑎−𝑏 𝑎−𝑎 𝑎−𝑏
18. If the error in the measurement of radius of a sphere is 2%, then the error in the determination of volume
of the sphere will be
a) 8% b) 2% c) 4% d) 6%
19. Out of the following four-dimensional quantities, which one qualifies to be called a dimensional constant?
a) Acceleration due to gravity b) Surface tension of water
c) Weight of a standard kilogram mass d) The velocity of light in vacuum
20. The values of two resistors are 𝑅$ = (6 ± 0.3)𝑘Ω and 𝑅! = (10 ± 0.2)𝑘Ω. The percentage error in the
equivalent resistance when they are connected in parallel is
a) 5.125% b) 2% c) 10.125% d) 7%
21. The dimensions of / in the equation 𝑃 = /#' ! , where 𝑃 is pressure, 𝑥 is distance and 𝑡 is time, are
& &0
a) 𝑀𝑇 #! b) 𝑀! 𝐿𝑇 #% c) 𝑀𝐿% 𝑇 #$ d) 𝐿𝑇 #%
22. A screw gauge gives the following reading when used to measure the diameter of a wire.
Main scale reading: 0 mm
Circular scale reading: 52 divisions
Given that 1 mm on main scale corresponds to
100 divisions of the circular scale.
The diameter of wire from the above data is
a) 0.052 cm b) 0.026 cm c) 0.005 cm d) 0.52 cm
/ 12
23. The equation of state of some gases can be expressed as ’𝑃 + “ = . Where 𝑃 is the pressure, 𝑉 the
+! +
volume, 𝜃 the absolute temperature and 𝑎 and 𝑏 are constants? The dimensional formula of 𝑎 is
a) [𝑀𝐿* 𝑇 #! ] b) [𝑀#$ 𝐿* 𝑇 #! ] c) [𝑀𝐿#$ 𝑇 #! ] d) [𝑀𝐿#* 𝑇 #! ]
24. The length of a cylinder is measured with a meter rod having least count 0.1 𝑐𝑚.
Its diameter is measured with vernier calipers having least count 0.01 𝑐𝑚. Given that length is 5.0 𝑐𝑚. and
radius is 2.0 𝑐𝑚. The percentage error in the calculated value of the volume will be
a) 1% b) 2% c) 3% d) 4%
25. If 𝐸 = energy, 𝐺 = gravitational constant, 𝐼 = impulse and 𝑀 = mass, then dimensions of 345! are same as
6!
that of
a) Time b) Mass c) Length d) Force
Chaudhary
, Units and Dimensions
1. In a vernier callipers, one main scale division is 𝑥 𝑐𝑚 and 𝑛 division of the vernier scale coincide with (𝑛 −
1) divisions of the main scale. The least count (in 𝑐𝑚) of the callipers is
𝑛−1 𝑛𝑥 𝑥 𝑥
a) @ A𝑥 b) c) d)
𝑛 (𝑛 − 1) 𝑛 (𝑛 − 1)
2. If the speed of light (𝑐), acceleration due to gravity (𝑔) and pressure (𝑝) are taken as the fundamental
quantities, then the dimension of gravitational constant is
a) 𝑐 ! 𝑔" 𝑝#! b) 𝑐 " 𝑔! 𝑝#$ c) 𝑐𝑔% 𝑝#! d) 𝑐 #$ 𝑔" 𝑝#$
3. Dimension of 𝑅 is
a) 𝑀𝐿! 𝑇 #$ b) 𝑀𝐿! 𝑇 #% 𝐴#! c) 𝑀𝐿#$ 𝑇 #! d) None of these
4. “Pascal-Second” has dimension of
a) Force b) Energy
c) Pressure d) Coefficient of viscosity
5. The unit of physical quantity obtained by the line integral of electric field is
a) NC#$ b) Vm#$ c) JC#$ d) C! N#$ m#!
6. The dimensions of electric potential are
a) [𝑀𝐿! 𝑇 #! 𝑄#$ ] b) [𝑀𝐿𝑇 #! 𝑄#$ ] c) [𝑀𝐿! 𝑇 #$ 𝑄] d) [𝑀𝐿! 𝑇 #! 𝑄]
7. &
The velocity 𝑣 (in 𝑐𝑚/𝑠𝑒𝑐) of a particle is given in terms of time 𝑡(in 𝑠𝑒𝑐) by the relation 𝑣 = 𝑎𝑡 + '() ; the
dimensions of 𝑎, 𝑏 and 𝑐 are
a) 𝑎 = 𝐿! , 𝑏 = 𝑇, 𝑐 = 𝐿𝑇 ! b) 𝑎 = 𝐿𝑇 ! , 𝑏 = 𝐿𝑇, 𝑐 = 𝐿
c) 𝑎 = 𝐿𝑇 ! , 𝑏 = 𝐿, 𝑐 = 𝑇 d) 𝑎 = 𝐿, 𝑏 = 𝐿𝑇, 𝑐 = 𝑇 !
8. A student measures the distance traversed in free fall of a body, initially at rest in each time. He uses this
data to estimate 𝑔, the acceleration due to gravity. If the maximum percentage errors in measurement of
the distance and the time are 𝑒$ and 𝑒! respectively, the percentage error in the estimation of 𝑔 is
a) 𝑒! − 𝑒$ b) 𝑒$ + 2𝑒! c) 𝑒$ + 𝑒! d) 𝑒$ − 2𝑒!
9. Which of the following is the smallest unit
a) 𝑀𝑖𝑙𝑙𝑖𝑚𝑒𝑡𝑟𝑒 b) 𝐴𝑛𝑔𝑠𝑡𝑟𝑜𝑚 c) 𝐹𝑒𝑟𝑚𝑖 d) 𝑀𝑒𝑡𝑟𝑒
10. Which relation is wrong
a) 1 𝑐𝑎𝑙𝑜𝑟𝑖𝑒 = 4.18 𝑗𝑜𝑢𝑙𝑒 b) 1 Å = 10#$" 𝑚
c) 1 𝑀𝑒𝑉 = 1.6 × 10#$% 𝑗𝑜𝑢𝑙𝑒 d) 1 𝑛𝑒𝑤𝑡𝑜𝑛 = 10#* 𝑑𝑦𝑛𝑒
+
11. The resistance 𝑅 = where 𝑉 = 100 ± 5 𝑣𝑜𝑙𝑡𝑠 and 𝑖 = 10 ± 0.2 𝑎𝑚𝑝𝑒𝑟𝑒𝑠. What is the total error in 𝑅
,
5
a) 5% b) 7% c) 5.2% d) %
2
12. A vernier calipers has 1 𝑚𝑚 marks on the main scale. It has 20 equal divisions on the Vernier scale which
match with 16 main scale divisions. For this Vernier callipers, the least count is
a) 0.02 𝑚𝑚 b) 0.05 𝑚𝑚 c) 0.1 𝑚𝑚 d) 0.2 𝑚𝑚
, 13. Given 𝑋 = (𝐺ℎ/𝑐 % )$/! , where 𝐺, ℎ and 𝑐 are gravitational constant, Planck’s constant and the velocity of
light respectively. Dimensions of 𝑋 are the same as those of
a) Mass b) Time c) Length d) Acceleration
14. Number of base SI unit is
a) 4 b) 7 c) 3 d) 5
15. The dimensions of permittivity 𝜀" are
a) 𝐴! 𝑇 ! 𝑀#$ 𝐿#% b) 𝐴! 𝑇 . 𝑀#$ 𝐿#% c) 𝐴#! 𝑇 #. 𝑀𝐿% d) 𝐴! 𝑇 #. 𝑀#$ 𝐿#%
16. Two full turns of the circular scale of a screw gauge cover 1 mm 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
17. If 𝑥 = 𝑎 − 𝑏, then the maximum percentage error in the measurement of 𝑥 will be
∆𝑎 + ∆𝑏 ∆𝑎 ∆𝑏
a) @ A × 100% b) @ − A × 100%
𝑎−𝑏 𝑎 𝑏
∆𝑎 ∆𝑏 ∆𝑎 ∆𝑏
c) @ + A × 100% d) @ − A × 100%
𝑎−𝑎 𝑎−𝑏 𝑎−𝑎 𝑎−𝑏
18. If the error in the measurement of radius of a sphere is 2%, then the error in the determination of volume
of the sphere will be
a) 8% b) 2% c) 4% d) 6%
19. Out of the following four-dimensional quantities, which one qualifies to be called a dimensional constant?
a) Acceleration due to gravity b) Surface tension of water
c) Weight of a standard kilogram mass d) The velocity of light in vacuum
20. The values of two resistors are 𝑅$ = (6 ± 0.3)𝑘Ω and 𝑅! = (10 ± 0.2)𝑘Ω. The percentage error in the
equivalent resistance when they are connected in parallel is
a) 5.125% b) 2% c) 10.125% d) 7%
21. The dimensions of / in the equation 𝑃 = /#' ! , where 𝑃 is pressure, 𝑥 is distance and 𝑡 is time, are
& &0
a) 𝑀𝑇 #! b) 𝑀! 𝐿𝑇 #% c) 𝑀𝐿% 𝑇 #$ d) 𝐿𝑇 #%
22. A screw gauge gives the following reading when used to measure the diameter of a wire.
Main scale reading: 0 mm
Circular scale reading: 52 divisions
Given that 1 mm on main scale corresponds to
100 divisions of the circular scale.
The diameter of wire from the above data is
a) 0.052 cm b) 0.026 cm c) 0.005 cm d) 0.52 cm
/ 12
23. The equation of state of some gases can be expressed as ’𝑃 + “ = . Where 𝑃 is the pressure, 𝑉 the
+! +
volume, 𝜃 the absolute temperature and 𝑎 and 𝑏 are constants? The dimensional formula of 𝑎 is
a) [𝑀𝐿* 𝑇 #! ] b) [𝑀#$ 𝐿* 𝑇 #! ] c) [𝑀𝐿#$ 𝑇 #! ] d) [𝑀𝐿#* 𝑇 #! ]
24. The length of a cylinder is measured with a meter rod having least count 0.1 𝑐𝑚.
Its diameter is measured with vernier calipers having least count 0.01 𝑐𝑚. Given that length is 5.0 𝑐𝑚. and
radius is 2.0 𝑐𝑚. The percentage error in the calculated value of the volume will be
a) 1% b) 2% c) 3% d) 4%
25. If 𝐸 = energy, 𝐺 = gravitational constant, 𝐼 = impulse and 𝑀 = mass, then dimensions of 345! are same as
6!
that of
a) Time b) Mass c) Length d) Force
