1.

Express the following in SI units : (i) 92 million miles (This is the distance between earth and sun) (ii) 90 miles per hour (the typical speed of Rajdhani express) (iii) 5 feet 4 inches (the average height of Indian female) (iv) 0.74 Ã… (the bond length of hydrogen molecule) (v) 45^(@)C (the peak summer temperature n Jaipur) (vi) 140 pounds (the average weight of Indian male).

Answer»

Solution :(i) The `SI` unit of distance = metre (m)
1 mile `= 1.60 km = 1.6 xx 10^(3)` m
Conversion FACTOR `= ((1.6xx10^(3)m))/(("1 mile"))`
92 million miles `=92xx10^(6)` miles
`92xx10^(6)` miles `=92xx10^(6)`miles `xx` conversion factor
`=(92xx10^(6) "miles")xx((1.6xx10^(3)m))/(("1 mile"))=147.2xx10^(9)m=1.47xx10^(11)m`
(ii) 1 mile `= 1.6 km = 1.6 xx 10^(3)` m
Conversion factor `= ((1.6xx10^(3)m))/(("1 mile"))`
1 hour `=60xx60s=3.6xx10^(3)s` ltbtgt Conversion factor `=((3.6xx10^(3)s))/(("1 HR"))`
We have two conversion factors for both the physical quantities i.e., distance and TIME
Speed `= ("90 miles")/("1 hr")=("90 miles"xx("conversion factor"))/("1 hr"xx("conversion factor"))`
`= ("90 miles")xx((1.6xx10^(3)m))/(("1 miles"))xx(1)/(("1 hr"))xx(("1 hr"))/((3.6xx10^(3)s))=(90xx1.6)/(3.6)ms^(-1)=40 ms^(-1)`
(iii) 5 feet and inches `= 5 xx 12 +4 = 64` inches , 1 inch `= 2.54 xx 10^(-2) m`
Conversion factor `= ((2.54xx10^(-2)m))/(("1 inch"))`
64 inches = 64 inches `xx` conversion factor
`= ("64 inches")xx((2.54xx10^(-2)m))/(("1 inch"))=1.63m`
(iv) `1 Ã… = 10^(-10) m`
Conversion factor `= (10^(-10)m)/(1 Ã…),0.74 Ã…=0.747xx` conversion factor
`=(0.74Ã…)xx((10^(-10)m))/((1Ã…))=0.74xx10^(-10)m=7.4xx10^(-11)m`
(v) `0^(@)C=273.15K`
`45^(@)C=273.15+45=318.15K`
(VI) 1 pound `= 453.6 xx 10^(-3)` kg
Conversion factor `= ((453.6xx10^(-3)kg))/(("1 pound"))`
140pounds=(140 pounds)`xx` conversion factor
`= ("140 pounds")xx((453.6xx10^(-3)kg))/(("1 pound"))`
`=140xx453.6xx10^(-3)kg=63504xx10^(-3)kg=63.5kg`.


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