401_Physics ProblemsTechnical Physics

401_Physics ProblemsTechnical Physics - Chapter 13 P13.58...

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Chapter 13 403 P13.58 (a) G has units Nm kg kg m m sk g m g 2 2 2 22 3 2 = ⋅⋅ = and dimensions G L TM 3 2 = . The speed of light has dimensions of c = L T , and Planck’s constant has the same dimensions as angular momentum or h = ML T 2 . We require Gch pqr = L , or L T M L T M L T L M T 10 0 32 2 ppp q q r r r −− = . Thus, 3 2 1 pq r ++ = − −−= −+= 20 0 pr which reduces (using rp = ) to 1 pq p −−−= pqp These equations simplify to 5 1 pq += and qp =− 3. Then, 531 pp −= , yielding p = 1 2 , q 3 2 , and r = 1
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