Question

G = 6.67 x 10⁻¹¹ N m² (kg)⁻² = _____(cm)³ s⁻² g⁻¹. Fill in the blank.

Answer 1

Answer:

$G\ =\ 6.67\times 10^{-2}\ (cm^3)s^{-2}g^{-1}$

Explanation:

Given,

* $N\ =\ \dfrac{kg m}{s^2}$

* 1 kg = 1000 g

* 1 m = 100 cm

$G\ =\ 6.67\times 10^{-11}\ \dfrac{Nm^2}{kg^2}\\\Rightarrow G\ =\ 6.67\times 10^{-11}\ \dfrac{kg m\times m^}{s^2\times kg^2}\\\Rightarrow G\ =\ 6.67\times 10^{-11}\ \dfrac{kgm^3}{s^2}\\\Rightarrow G\ =\ 6.67\times 10^{-11}\ \dfrac{10^3\ g\times 10^6\ cm^3}{s^2}\\\Rightarrow G\ =\ 6.67\times 10^{-2}\ (cm^3)s^{-2}g^{-1}$

Answer 2

Answer:

$6.67 \times 10^{-8} \left ( cm \right )^{3}\left ( s \right )^{-2}\left ( g \right )^{-1}$

Explanation:

given G = $6.67 \times 10^{-11} Nm^{2} (kg)^{-2}$

now we know that

$1 N = 1 \frac{kg-m}{s^{2} }$

1m = 100 cm

1kg = 1000 gm

put these value in above equation

∴ G = $6.67 \times 10^{-11} Nm^{2} (kg)^{-2}$

      = $6.67 \times 10^{-11} \frac{m^{3}}{s^{2}-kg}$

      = $6.67 \times 10^{-11} \frac{\left ( 100cm \right )^{3}}{s^{2}-\left ( 1000 gm \right )}$

      = $6.67 \times 10^{-8} \left ( cm \right )^{3}\left ( s \right )^{-2}\left ( g \right )^{-1}$