Let the universal gravitational constant have the value N m kg in SI units

PHYSICS · Multi-part · A Level · Physics · Measurements and their errors · Measurements and their errors

Problem

Let the universal gravitational constant have the value G=6.67×10−11G = 6.67 \times 10^{-11} N m2^{2} kg−2^{-2} in SI units. A research group introduces a set of base units defined by Length   L∗=0.50 m\;L^{\ast} = 0.50\,\text{m}, Mass   M∗=200 g\;M^{\ast} = 200\,\text{g}, Time   T∗=0.020 s\;T^{\ast} = 0.020\,\text{s}. Answer the following: (i) Determine the numerical value of GG in the group’s own system of units. (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 GG because of this mistake.

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