StudentAidUnit 1: Physical Quantities and Measurements — Numericals
9th Class Physics · Unit 1: Physical Quantities and Measurements
1.1.Calculate the number of seconds in a (a) day (b) week (c) month and state your answers using SI prefixes.
Given
(a)
1 day = 24 hours
(a)
1 hour = 60 minutes
(a)
1 minute = 60 seconds
(a)
Seconds in a day = 1 × 24 × 60 × 60 s
(a)
= 86400 s
(a)
= 86.400 × 103 s
(a)
As 1k = 103 so, = 86.4k s
(b)
1 week = 7 days
(b)
1 day = 24 hours
(b)
1 hour = 60 minutes
(b)
1 minute = 60 seconds
(b)
Seconds in a week = 7 × 24 × 60 × 60 s
(b)
= 604800 s
(b)
= 604.8 × 103 s
(b)
= 604.8k s
(b)
As 1k = 103 so, = 604.8k s
(c)
1 month = 30 days
(c)
1 day = 24 hours
(c)
1 hour = 60 minutes
(c)
1 minute = 60 seconds
(c)
Seconds in a month = 30 × 24 × 60 × 60 s
(c)
= 2,592,000 s
(c)
= 2.592 × 106 s
(c)
As 106 = 1M so, = 2.592 M s
(a) 86.4k s; (b) 604.8k s; (c) 2.592 M s
1.2.State the answer of problem 1.1 in scientific notation.
Result
(a)
Seconds in a day = 8.64 × 104 s
(b)
Seconds in a week = 6.048 × 105 s
(c)
Seconds in a month = 2.592 × 106 s
1.3.Solve the following addition or subtraction. State your answers in scientific notation. (a) 4 × 10⁻⁴ kg + 3 ×10⁻⁵ kg (b) 5.4 × 10⁻⁶ m − 3.2 × 10⁻⁵ m
Given
(a)
4 × 10-4 kg = 0.0004 kg
(a)
3 × 10-5 kg = 0.00003 kg
(a)
By adding both equations: 0.0004 kg + 0.00003 kg
(a)
= 0.00043 kg
Result
(a)
Converting in scientific notation = 4.3 × 10-4 kg
Given
(b)
5.4 × 10-6 m = 0.0000054 m
(b)
3.2 × 10-5 m = 0.000032 m
Original text incorrectly shows 'kg' instead of 'm' in the working lines
(b)
By subtracting both equations: 0.0000054 m - 0.000032 m
(b)
= -0.0000266 m
Result
(b)
Converting in scientific notation = -2.66 × 10-5 m
1.4.Solve the following multiplication or division. State your answers in scientific notation. (a) (5 × 10⁴m) × (3 × 10⁻²m) (b) 6×10⁸kg / (3×10⁴m³)
(a)
= (5 × 104 m) × (3 × 10-2 m)
(a)
= (5 × 3)(104 × 10-2)(m × m)
(a)
= (15)(104-2)(m2)
(a)
= (1.5 × 101)(102)(m2)
(a)
= 1.5 × 101+2 m2
Result
(a)
= 1.5 × 103 m2
(b)
= frac{6 × 108 kg{3 × 104 m3}
(b)
= 63 × (108 × 10-4)(kg m-3)
(b)
= 2(108-4)(kg m-3)
(b)
= 2.0 × 104 kg m-3
1.5.Calculate the following and state your answer in scientific notation. \frac{(3 \times 10^2 \text{ kg}) \times (4.0 \text{ km})}{5 \times 10^2 \text{ s}^2}
Given
Expression
frac{(3 × 102 kg) × (4.0 km)}{5 × 102 s2
Result
Answer
= 2.4 × 103 kg m s-2
1.6.State the number of significant digits in each measurement. (a) 0.0045m (b) 2.047 m (c) 3.40m (d) 3.420 × 10⁴m
Result
(a)
0.0045 m has textbf{2} significant digits
(a)
Zeros for spacing purposes are not significant
(b)
2.047 m has textbf{4} significant figures
(b)
Zeros between significant figures are also significant
(c)
3.40 m has textbf{3} significant figures
(c)
Zero at right side of decimal value is also significant
(d)
3.420 × 104 m has textbf{4} significant figures
1.7.Write in scientific notation: (a) 0.0035m (b) 206.4 × 10²m
Result
(a)
0.0035 m = 3.5 × 10-3 m
(b)
206.4 × 102 m = 2.064 × 104 m
1.8.Write using correct prefixes: (a) 5.0 × 10⁴cm (b) 580 × 10²g (c) 45 × 10⁻⁴s
Given
(a)
5.0 × 104 cm
(a)
Since 1 cm = 10-2 m
(a)
= 5 × 104 × 10-2 m
(a)
= 5 × 104-2 m
(a)
= 5 × 102 m
(a)
= 0.5 × 101 × 102 m
(a)
= 0.5 × 101+2 m
(a)
= 0.5 × 103 m
(a)
Since 103 m = 1 km
Result
(a)
= 0.5 km
Given
(b)
580 × 102 g
(b)
= 58 × 101 × 102 g
(b)
= 58 × 101+2 g
(b)
= 58 × 103 g
(b)
Since 103 g = 1 kg
Result
(b)
= 58 kg
Given
(c)
45 × 10-4 s
(c)
= 4.5 × 101 × 10-4 s
(c)
= 4.5 × 101-4 s
(c)
= 4.5 × 10-3 s
(c)
Since 10-3 = 1 m
Result
(c)
= 4.5 ms
1.9.Light year is a unit of distance used in astronomy. It is the distance covered by light in one year. Taking the speed of light as 3.0 × 10⁸ms⁻¹, calculate the distance.
Given
Speed of light = v = 3 × 108 m s-1
Time = t = 1 year = 365 × 24 × 60 × 60 s
= 31,536,000 s
Formula
Distance = S = v × t
Working
S = (3 × 108)(31,536,000)
Result
= 9.46 × 1015 m
1.10.Express the density of mercury given as 13.6 g cm⁻³ in kg m⁻³.
Given
Density of mercury = D = 13.6 g cm-3
Formula
To Find: Density in kg m-3
As, 1 g cm-3 = 1000 kg m-3
So, 13.6 g cm-3 = 1000 × 13.6
= 13600 kg m-3
Result
= 1.36 × 104 kg m-3