Class 11 Physics Chapter 1: Units and Measurement worksheet with answer key
A 20-mark worksheet on Units and Measurement for about 40 minutes of class or homework: 5 multiple-choice, 3 very short answer and 3 short answer questions, written from the NCERT chapter and checked by a second reviewer. Print the PDF for the class; the answer key carries the marking scheme. Teachers may photocopy it freely.
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Answer: (c) It should be 22.2 g, since 3.1 g has only one decimal place.
The arithmetic sum is 22.177 g. In addition the result keeps as many decimal places as the least precise term, 3.1 g with one decimal place, so the total is 22.2 g. The significant-figure rule of (b) is the rule for multiplication and division, not for addition.
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Answer: (a) 0.00203 s
0.00203 s: the leading zeros only place the decimal point, so 2, 0, 3 count: three. 0.04050 kg has four (4, 0, 5 and the trailing zero after the decimal point); 3.070 m has four; 2.300 × 10³ g has four, since every zero in the base number of scientific notation is significant.
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Answer: (c) 2
In multiplication the result keeps as many significant figures as the factor with the fewest: 4.2 m has two. So 52.92 m² must be reported as 53 m², and the last two digits written, 9 and 2, are not justified.
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Answer: (d) 2
In a number without a decimal point the trailing zeros are not significant, so only 3 and 6 count: two significant figures.
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Answer: (b) 6.38
The digit dropped is 5 and the preceding digit, 7, is odd, so it is raised by 1: 6.38. (Had the preceding digit been even, the 5 would simply be dropped.)
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Force has dimensions [M L T⁻²], so a = 1, b = 1, c = −2. n₂ = n₁ [M₁/M₂]¹ [L₁/L₂]¹ [T₁/T₂]⁻² = 1 × (1 kg/1 g) × (1 m/1 cm) × 1 = 1000 × 100 = 10⁵. So 1 N = 10⁵ dyne.
- dimensions [M L T⁻²] and the conversion formula set up (1)
- 1 N = 10⁵ dyne (1)
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(a) The metre: the speed of light in vacuum c, fixed at 299792458 in m s⁻¹. (b) The kilogram: the Planck constant h, fixed at 6.62607015 × 10⁻³⁴ in J s (= kg m² s⁻¹).
- metre: speed of light c, in m s⁻¹ (1)
- kilogram: Planck constant h, in J s or kg m² s⁻¹ (1)
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(a) mole, mol; (b) candela, cd. One mole contains exactly 6.02214076 × 10²³ elementary entities, and these may be atoms, molecules, ions, electrons or other particles; a mole of hydrogen atoms is not the same amount of matter as a mole of hydrogen molecules, so the entity must be named.
- mole (mol) and candela (cd) (1)
- the entities may be atoms, molecules, ions etc., so the count is meaningless unless they are specified (1)
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(a) In a number without a decimal point the trailing zeros are not significant, so 7200 m reads as two significant figures, though the surveyor's reading has four. (b) 7.200 × 10³ m: zeros in the base number are significant, so four figures are shown. (c) 7.200 km; a change of units does not change the number of significant figures.
- trailing zeros without a decimal point read as not significant (1)
- 7.200 × 10³ m (1)
- 7.200 km (1)
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(a) Stress, and so the modulus, has dimensions [M L⁻¹ T⁻²]: a = 1, b = −1, c = −2. (b) M₁/M₂ = 1 kg/1 g = 1000; L₁/L₂ = 1 m/1 cm = 100; T₁/T₂ = 1. n₂ = 2.0 × 10¹¹ × 1000 × (100)⁻¹ = 2.0 × 10¹² dyne cm⁻²: Arjun is right. (c) 2.0 × 10¹¹ × 1000 × 100 = 2.0 × 10¹⁶: Kabir took b = +1, the power of L in force, and forgot the area in the denominator, which makes the power of L −1.
- a = 1, b = −1, c = −2 (1)
- 2.0 × 10¹¹ × 1000 × (100)⁻¹ = 2.0 × 10¹² dyne cm⁻²; Arjun right (1)
- Kabir used b = +1 (ignored the m⁻² of area) (1)
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(a) [M L T⁻²][T] = [M L T⁻¹], the same as linear momentum. (b) [M L T⁻²][L] = [M L² T⁻²], the same as work or energy. (c) [M L T⁻²]/[L²] = [M L⁻¹ T⁻²], the same as stress or modulus of elasticity.
- impulse [M L T⁻¹], momentum (1)
- torque [M L² T⁻²], work or energy (1)
- pressure [M L⁻¹ T⁻²], stress or modulus (1)