Question

Fill in the blanks

(a) 1 $kg{m}^2/s^2=.........gc{m}^2/s^2$

(b) 1 m = .......... ly

(c) 3.0 m $s^{-2}$ = .........km $h^{-2}$

(d) G = 6.67 $\times$ ${10}^{-11}$ N $m^2$ $(kg{)}^{-2}$ = .......... $(cm{)}^3$ $s^{-2}$ $g^{-1}$

Answer 1

(a)

$1kg{m}^2/s^2=1000gm\times (100cm{)}^2/s^2$

$={10}^{7}gc{m}^2/s^2$

(b)

$1ly=(365\times 24\times 3600)s\times (3\times {10}^8)m/s$

$1ly=9460730472580800metres\left(exactly\right)$

$1m={10}^{-16}ly$

(c)

$3m/s^2=3\times \left({10}^{-3}km\right)\times (1/3600h{)}^{-2}$

$=3\times {3600}^2\times {10}^{-3}km{h}^{-2}$

$=38880km{h}^{-2}$

(d)

$G=6.67\times {10}^{-11}N{m}^{2}k{g}^{-2}$

$=6.67\times {10}^{-11}kgm/s^2{m}^{2}k{g}^{-2}$

$=6.67\times {10}^{-11}{s}^{-2}{m}^{3}k{g}^{-1}$

$=6.67\times {10}^{-11}{s}^{-2}\times (100cm{)}^3/1000g$

$=6.67\times {10}^{-11}{s}^{-2}\times {10}^{6}c{m}^3/1000g$

$=6.67\times {10}^{-8}{s}^{-2}c{m}^3{g}^{-1}$