Physics

Problem

Let the universal gravitational constant have the value

G = 6.67 \times 10^{-11}

N m

^{2}

^{-2}

in SI units. A research group introduces a set of base units defined by Length

\;L^{\ast} = 0.50\,\text{m}

, Mass

\;M^{\ast} = 200\,\text{g}

, Time

\;T^{\ast} = 0.020\,\text{s}

. Answer the following: a. (i) Determine the numerical value of

G

in the group’s own system of units. b. (ii) Suppose a student by oversight keeps the SI second instead of the new time unit while converting. Calculate the percentage error introduced in the value of

G

because of this mistake.

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