(a) (i) Define the Dimensional Consistency in a formula. (ii) The Gravitational force F exerted between two arbitrary masses m, and m, is given by F Gm where 1* is the distance between two centers of mases m and m and G is the gravitational constant. Show that G is dimensionally consistent. (iii) Let be the time, P be the pressure, I be the distance, m be the mass. Some physicists claims that he theoretically discovered the formula Pm 51n (3k) where k is a positive constant. Is the physicist's formulae valid? Justify your answer. (b) (i) Let be the distance, and v be its velocity, g be the gravitational acceleration. Suppose a particle which is at rest in the air is falling to a horizontal plane under the gravitational force with a vertical distance to the plane. It was observed that his proportional to v and g. Using the principles of dimensional analysis, derive a and g. formula for the distance h in terms of (ii) Are the following formulas dimensionally consistent? Justify your answers in each case. are accelerations, h is a distance, v,u are velocities and I is the time. Note that a.g v-u (a) a 3h (v-2u) (b) sin=- 3g = (c) 3h 2ut+- 10 1