qz1sp08sol - January18,2008 PHY2053Discussion...

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January 18, 2008 PHY2053 Discussion Quiz 1 (Chapter 1 & 2.1-2.4) Name:                                   UFID: *1. (5 pts) Newton’s law of universal gravitation is represented by  F = GMm/r ² , where  F   is the gravitational force,   M   and   m   are masses, and   r   is a length. What is the  dimension of the proportionality constant   G   ? (Hint: Force is given by mass times  acceleration.) Since the dimension of both sides should be the same, we get [F] = [G][Mm]/[r ² ]. Plug [F] = [M][a] = MLTˉ ² , [Mm] = M ²  and [r ² ] = L ²  into the equation, and solve it for   [G]: MLTˉ ²  = [G]M ² /L ²    [G] = Mˉ ¹ L ³ ² ***2. (5 pts) Two boats start together and race across 50 km-wide lake and back. The  boat that completes the round trip first wins. Boat A goes across at 40 km/h and  returns at 40km/h. Boat B goes across at 30km/h at first, but it doubles its speed when 
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