JEE Physics Units and Measurements MCQs Set 20

Answer: (c) Light year, time period

Explanation:
1. Potential gradient and electric field are both V/m, and torque and energy are both \( [ML^2T^{-2}] \).
2. Impedance and reactance are both in ohm.
3. A light year is a length, while a time period is a time, so (c) differs.

Teacher's Note:
1. L
2. i
3. g
4. h
5. t
6.
7. y
8. e
9. a
10. r
11.
12. i
13. s
14.
15. a
16.
17. d
18. i
19. s
20. t
21. a
22. n
23. c
24. e
25.
26. t
27. r
28. a
29. v
30. e
31. l
32. l
33. e
34. d
35.
36. b
37. y
38.
39. l
40. i
41. g
42. h
43. t
44.
45. i
46. n
47.
48. a
49.
50. y
51. e
52. a
53. r
54. .
55.
56. C
57. h
58. e
59. c
60. k
61.
62. w
63. h
64. i
65. c
66. h
67.
68. p
69. a
70. i
71. r
72. s
73.
74. a
75. r
76. e
77.
78. o
79. n
80. l
81. y
82.
83. c
84. a
85. l
86. l
87. e
88. d
89.
90. b
91. y
92.
93. s
94. i
95. m
96. i
97. l
98. a
99. r
100.
101. n
102. a
103. m
104. e
105. s
106. .

Answer: (a) \( [ML^2T^{-2}] \)

Explanation:
1. Torque = force × perpendicular distance.
2. \( [\tau]=MLT^{-2}\times L=ML^2T^{-2} \).

Teacher's Note:
1. T
2. o
3. r
4. q
5. u
6. e
7.
8. h
9. a
10. s
11.
12. t
13. h
14. e
15.
16. s
17. a
18. m
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20.
21. d
22. i
23. m
24. e
25. n
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27. i
28. o
29. n
30. s
31.
32. a
33. s
34.
35. w
36. o
37. r
38. k
39.
40. a
41. n
42. d
43.
44. e
45. n
46. e
47. r
48. g
49. y
50. ,
51.
52. b
53. u
54. t
55.
56. i
57. t
58.
59. i
60. s
61.
62. a
63.
64. d
65. i
66. f
67. f
68. e
69. r
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73.
74. p
75. h
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77. s
78. i
79. c
80. a
81. l
82.
83. q
84. u
85. a
86. n
87. t
88. i
89. t
90. y
91. .

Answer: (c) \( 2x+y \)

Explanation:
1. \( g=\dfrac{4\pi^2\ell}{T^2} \).
2. Maximum fractional error: \( \dfrac{\Delta g}{g}=\dfrac{\Delta\ell}{\ell}+2\dfrac{\Delta T}{T}=y+2x \).

Teacher's Note:
1. F
2. o
3. r
4.
5. q
6. u
7. o
8. t
9. i
10. e
11. n
12. t
13. s
14.
15. a
16. n
17. d
18.
19. p
20. o
21. w
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23. r
24. s
25. ,
26.
27. f
28. r
29. a
30. c
31. t
32. i
33. o
34. n
35. a
36. l
37.
38. e
39. r
40. r
41. o
42. r
43. s
44.
45. a
46. d
47. d
48. ,
49.
50. w
51. i
52. t
53. h
54.
55. e
56. a
57. c
58. h
59.
60. m
61. u
62. l
63. t
64. i
65. p
66. l
67. i
68. e
69. d
70.
71. b
72. y
73.
74. i
75. t
76. s
77.
78. p
79. o
80. w
81. e
82. r
83. .
84.
85. E
86. r
87. r
88. o
89. r
90. s
91.
92. n
93. e
94. v
95. e
96. r
97.
98. s
99. u
100. b
101. t
102. r
103. a
104. c
105. t
106.
107. i
108. n
109.
110. t
111. h
112. e
113.
114. m
115. a
116. x
117. i
118. m
119. u
120. m
121.
122. e
123. s
124. t
125. i
126. m
127. a
128. t
129. e
130. .

Answer: (b) \( [M^{-1}L^{-2}T^2Q^2] \)

Explanation:
1. \( C=Q/V \) and \( V=W/Q=ML^2T^{-2}Q^{-1} \).
2. \( [C]=\dfrac{Q}{ML^2T^{-2}Q^{-1}}=M^{-1}L^{-2}T^2Q^2 \).

Teacher's Note:
1. C
2. a
3. p
4. a
5. c
6. i
7. t
8. a
9. n
10. c
11. e
12.
13. i
14. s
15.
16. c
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18. a
19. r
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22. ²
23.
24. p
25. e
26. r
27.
28. e
29. n
30. e
31. r
32. g
33. y
34. .
35.
36. I
37. n
38.
39. t
40. e
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42. m
43. s
44.
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47.
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50. r
51. r
52. e
53. n
54. t
55.
56. i
57. t
58.
59. i
60. s
61.
62. M
63. ⁻
64. ¹
65. L
66. ⁻
67. ²
68. T
69. ⁴
70. A
71. ²
72. .

Answer: (d) 13%

Explanation:
1. \( \rho=m/L^3 \).
2. Maximum percentage error = 4% + 3 × 3% = 13%.

Teacher's Note:
1. T
2. h
3. e
4.
5. p
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10.
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50. g
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77. i
78. b
79. u
80. t
81. i
82. o
83. n
84. s
85. .

Answer: (c) \( [ML^{-1}T^{-2}] \)

Explanation:
1. The expression is the energy density of an electric field, energy per unit volume.
2. \( [u]=\dfrac{ML^2T^{-2}}{L^3}=ML^{-1}T^{-2} \).

Teacher's Note:
1. E
2. n
3. e
4. r
5. g
6. y
7.
8. d
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11. s
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19.
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44. r
45. e
46. .
47.
48. I
49. t
50.
51. i
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53.
54. ½
55. ε
56. ₀
57. E
58. ²
59.
60. f
61. o
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63.
64. a
65. n
66.
67. e
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69. e
70. c
71. t
72. r
73. i
74. c
75.
76. f
77. i
78. e
79. l
80. d
81. .

Answer: (c) 0.8%

Explanation:
1. Error in time = least count = 0.2 s.
2. Percentage error = \( \dfrac{0.2}{25}\times100=0.8 \)%.

Teacher's Note:
1. T
2. h
3. e
4.
5. l
6. e
7. a
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9. t
10.
11. c
12. o
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21. h
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25. a
26. x
27. i
28. m
29. u
30. m
31.
32. e
33. r
34. r
35. o
36. r
37.
38. i
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40.
41. a
42.
43. s
44. i
45. n
46. g
47. l
48. e
49.
50. r
51. e
52. a
53. d
54. i
55. n
56. g
57. .
58.
59. P
60. e
61. r
62. c
63. e
64. n
65. t
66. a
67. g
68. e
69.
70. e
71. r
72. r
73. o
74. r
75.
76. i
77. s
78.
79. Δ
80. t
81. /
82. t
83.
84. ×
85.
86. 1
87. 0
88. 0
89. .

Answer: (c) Boltzmann constant

Explanation:
1. eV is energy, so eV/T is energy per kelvin.
2. Boltzmann's constant \( k=E/T \) has the unit J K⁻¹.

Teacher's Note:
1. B
2. o
3. l
4. t
5. z
6. m
7. a
8. n
9. n
10. '
11. s
12.
13. c
14. o
15. n
16. s
17. t
18. a
19. n
20. t
21.
22. r
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24. l
25. a
26. t
27. e
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29.
30. e
31. n
32. e
33. r
34. g
35. y
36.
37. t
38. o
39.
40. t
41. e
42. m
43. p
44. e
45. r
46. a
47. t
48. u
49. r
50. e
51. .
52.
53. S
54. t
55. e
56. f
57. a
58. n
59. '
60. s
61.
62. c
63. o
64. n
65. s
66. t
67. a
68. n
69. t
70.
71. h
72. a
73. s
74.
75. u
76. n
77. i
78. t
79. s
80.
81. W
82.
83. m
84. ⁻
85. ²
86.
87. K
88. ⁻
89. ⁴
90. .

Answer: (d) \( u=\dfrac{e^2a_0}{hc} \)

Explanation:
1. Let \( u=e^a a_0^b h^c c^d \). Capacitance has dimensions \( M^{-1}L^{-2}T^2Q^2 \).
2. Charge: a = 2. Mass: c = −1. Time: −c − d = 2 gives d = −1. Length: b + 2c + d = −2 gives b = 1.
3. So \( u=\dfrac{e^2a_0}{hc} \).

Teacher's Note:
1. C
2. o
3. m
4. p
5. a
6. r
7. e
8.
9. p
10. o
11. w
12. e
13. r
14. s
15.
16. o
17. f
18.
19. Q
20. ,
21.
22. M
23. ,
24.
25. T
26.
27. a
28. n
29. d
30.
31. L
32.
33. o
34. n
35. e
36.
37. b
38. y
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42. e
43. .
44.
45. S
46. o
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48. v
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50.
51. i
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53.
54. t
55. h
56. a
57. t
58.
59. o
60. r
61. d
62. e
63. r
64. ,
65.
66. s
67. i
68. n
69. c
70. e
71.
72. e
73. a
74. c
75. h
76.
77. s
78. t
79. e
80. p
81.
82. i
83. n
84. v
85. o
86. l
87. v
88. e
89. s
90.
91. o
92. n
93. e
94.
95. n
96. e
97. w
98.
99. u
100. n
101. k
102. n
103. o
104. w
105. n
106. .

Answer: (d) 8%

Explanation:
1. \( P=F/L^2 \).
2. Maximum error = 4% + 2 × 2% = 8%.

Teacher's Note:
1. A
2.
3. s
4. q
5. u
6. a
7. r
8. e
9.
10. p
11. o
12. w
13. e
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44. e
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47. a
48. g
49. e
50.
51. e
52. r
53. r
54. o
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57.
58. A
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60. d
61.
62. a
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65.
66. c
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69. t
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79.
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85. h
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90. x
91. i
92. m
93. u
94. m
95.
96. e
97. r
98. r
99. o
100. r
101. .

Answer: (c) A is true, but R is false.

Explanation:
1. Both relative velocity and change in velocity are velocities, dimension \( [LT^{-1}] \), so the assertion is true.
2. Relative velocity is the vector difference of the two velocities, not their ratio, so the reason is false.

Teacher's Note:
1. A
2.
3. r
4. a
5. t
6. i
7. o
8.
9. o
10. f
11.
12. v
13. e
14. l
15. o
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27. d
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33. i
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35. e
36. n
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38. i
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40. n
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42. e
43. s
44. s
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46.
47. R
48. e
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50. a
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52. i
53. v
54. e
55.
56. v
57. e
58. l
59. o
60. c
61. i
62. t
63. y
64.
65. =
66.
67. v
68. _
69. P
70.
71. −
72.
73. v
74. _
75. Q
76. .

Answer: (a) Both A and R are true, and R is the correct explanation of A.

Explanation:
1. Specific gravity is the ratio of two densities, so the dimensions cancel and it is dimensionless.
2. The reason states this ratio, so both are true and the reason explains the assertion.

Teacher's Note:
1. R
2. a
3. t
4. i
5. o
6. s
7.
8. o
9. f
10.
11. l
12. i
13. k
14. e
15.
16. q
17. u
18. a
19. n
20. t
21. i
22. t
23. i
24. e
25. s
26.
27. s
28. u
29. c
30. h
31.
32. a
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34.
35. s
36. t
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38. a
39. i
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42.
43. r
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45. f
46. r
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50. i
51. v
52. e
53.
54. i
55. n
56. d
57. e
58. x
59.
60. a
61. n
62. d
63.
64. s
65. p
66. e
67. c
68. i
69. f
70. i
71. c
72.
73. g
74. r
75. a
76. v
77. i
78. t
79. y
80.
81. h
82. a
83. v
84. e
85.
86. n
87. o
88.
89. d
90. i
91. m
92. e
93. n
94. s
95. i
96. o
97. n
98. s
99. .

Answer: (c) A is true, but R is false.

Explanation:
1. Surface area \( A=4\pi r^2 \) so \( \dfrac{\Delta A}{A}=\dfrac{2\Delta r}{r}=2\times0.3=0.6 \)%. The assertion is true.
2. The formula given in the reason has the factor 4 instead of 2, so the reason is false.

Teacher's Note:
1. T
2. h
3. e
4.
5. c
6. o
7. n
8. s
9. t
10. a
11. n
12. t
13.
14. 4
15. π
16.
17. d
18. o
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20. s
21.
22. n
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25.
26. c
27. o
28. n
29. t
30. r
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51. n
52. a
53. l
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58. o
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61.
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65. y
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75. r
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77. o
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79.
80. r
81.
82. (
83. h
84. e
85. r
86. e
87.
88. 2
89. )
90.
91. m
92. a
93. t
94. t
95. e
96. r
97. s
98. .

Answer: (a) Both A and R are true, and R is the correct explanation of A.

Explanation:
1. Kinetic energy \( E=\tfrac12mv^2 \), so \( \dfrac{\Delta E}{E}=\dfrac{\Delta m}{m}+\dfrac{2\Delta v}{v} \) (reason true).
2. Error = 1% + 2 × 2% = 5% (assertion true) and the formula explains it.

Teacher's Note:
1. T
2. h
3. e
4.
5. p
6. o
7. w
8. e
9. r
10.
11. o
12. f
13.
14. e
15. a
16. c
17. h
18.
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20. a
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23. a
24. b
25. l
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34. l
35. i
36. e
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38.
39. i
40. t
41. s
42.
43. f
44. r
45. a
46. c
47. t
48. i
49. o
50. n
51. a
52. l
53.
54. e
55. r
56. r
57. o
58. r
59. .
60.
61. K
62. E
63.
64. h
65. a
66. s
67.
68. v
69. ²
70. ,
71.
72. s
73. o
74.
75. t
76. h
77. e
78.
79. v
80. e
81. l
82. o
83. c
84. i
85. t
86. y
87.
88. e
89. r
90. r
91. o
92. r
93.
94. c
95. o
96. u
97. n
98. t
99. s
100.
101. d
102. o
103. u
104. b
105. l
106. e
107. .

Answer: (b) Both A and R are true, but R is not the correct explanation of A.

Explanation:
1. A smaller least count allows more digits to be recorded, so the assertion is true.
2. The number of significant figures indicates the accuracy of the measurement, so the reason is also true.
3. However, it does not explain why the count depends on the least count, so it is not the explanation.

Teacher's Note:
1. M
2. o
3. r
4. e
5.
6. s
7. i
8. g
9. n
10. i
11. f
12. i
13. c
14. a
15. n
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17.
18. f
19. i
20. g
21. u
22. r
23. e
24. s
25.
26. c
27. o
28. r
29. r
30. e
31. s
32. p
33. o
34. n
35. d
36.
37. t
38. o
39.
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41.
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43. m
44. a
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46. l
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50. l
51. e
52. a
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55.
56. c
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60. t
61.
62. a
63. n
64. d
65.
66. a
67.
68. m
69. o
70. r
71. e
72.
73. p
74. r
75. e
76. c
77. i
78. s
79. e
80.
81. m
82. e
83. a
84. s
85. u
86. r
87. e
88. m
89. e
90. n
91. t
92. .

Answer: (b) Both A and R are true, but R is not the correct explanation of A.

Explanation:
1. Quantities can be measured directly with instruments (such as length) or calculated from other measurements (such as density), so the assertion is true.
2. Accuracy and precision of the instrument and errors must be reported with the result, so the reason is true.
3. The reason does not explain why both methods are used, so it is not the explanation.

Teacher's Note:
1. A
2. n
3. y
4.
5. r
6. e
7. s
8. u
9. l
10. t
11.
12. s
13. h
14. o
15. u
16. l
17. d
18.
19. b
20. e
21.
22. q
23. u
24. o
25. t
26. e
27. d
28.
29. w
30. i
31. t
32. h
33.
34. i
35. t
36. s
37.
38. e
39. r
40. r
41. o
42. r
43.
44. a
45. n
46. d
47.
48. t
49. h
50. e
51.
52. p
53. r
54. o
55. p
56. e
57. r
58.
59. n
60. u
61. m
62. b
63. e
64. r
65.
66. o
67. f
68.
69. s
70. i
71. g
72. n
73. i
74. f
75. i
76. c
77. a
78. n
79. t
80.
81. f
82. i
83. g
84. u
85. r
86. e
87. s
88. .
89.
90. T
91. h
92. i
93. s
94.
95. i
96. s
97.
98. t
99. r
100. u
101. e
102.
103. w
104. h
105. e
106. t
107. h
108. e
109. r
110.
111. t
112. h
113. e
114.
115. m
116. e
117. a
118. s
119. u
120. r
121. e
122. m
123. e
124. n
125. t
126.
127. i
128. s
129.
130. d
131. i
132. r
133. e
134. c
135. t
136.
137. o
138. r
139.
140. i
141. n
142. d
143. i
144. r
145. e
146. c
147. t
148. .