b) Given: A = 70.1 cm, B= 12.65 N, C=2.05 ft, D = 10.2 s, and E = 0.05 kg, analyze the
following mathematical operations by performing dimensional analysis and determine P, Q,
R, and S if the operations are permissible, and report your answer with appropriate S/ units
and the proper number of significant digits.
[11 marks]
(i) P=A+C
=L+L (permissible)
70.1 cm + 2.05 ft \frac{0.3048 m}{1 ft} \frac{100 cm}{1 m} = 132.6 cm [Ans]
(ii) Q = B - (AE)
= \frac{MLT^{-2}}{ML} = T^{-2} (permissible)
\frac{12.65 N}{0.701 m (0.05 kg)} = 360.91 \approx 3.61 \times 10^2 \frac{N}{kg \cdot m} or s^{-2} [Ans]
