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1.Units, Dimensions and Measurement
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In a particular system the units of length, mass and time are chosen to be $10\;cm , 10 \;g$, and $0.1\;s$ respectively. The units of force in this system will be equal to?
A$0.1$
B$1 $
C$10 $
D$100$
Solution
$1 newton =1 kgm / s ^{2}$
$1 kg =10^{3}$ and $1 m =10^{2} cm$
$1 N =\frac{\left(10^{3} g \right)\left(10^{2} cm \right)}{ s ^{2}}$
$1 N =\frac{100 \times(10 g ) \times 10(10 cm )}{100 \times(0.1 s )^{2}}$
$=10 \times \frac{(10 g )(10 cm )}{(0.1 s )^{2}}$
$1 N =10 \times$ New unit of force Thus, New unit $=1 / 10=0.1 N$
$1 kg =10^{3}$ and $1 m =10^{2} cm$
$1 N =\frac{\left(10^{3} g \right)\left(10^{2} cm \right)}{ s ^{2}}$
$1 N =\frac{100 \times(10 g ) \times 10(10 cm )}{100 \times(0.1 s )^{2}}$
$=10 \times \frac{(10 g )(10 cm )}{(0.1 s )^{2}}$
$1 N =10 \times$ New unit of force Thus, New unit $=1 / 10=0.1 N$
Standard 11
Physics
