91Ó°ÊÓ

Gravitational potential: The gravitational potential energy is stored in the body due to virtue of its position.

The expression of gravitational energy is given as,

$E_p=mgh$ (1.1)

Here, m is the mass of the object, g is the acceleration due to gravity, h is the height the object is lifted up from the surface of Earth.

(a)

Considering the given values,

Putting$7×{10}^9\text{kg}$ for m,$9.8\text{m}/{\text{s}}^2$ for g, and 36.5 m for h in equation (1.1),

$\begin{array}{rcl}{E}_p& =& \left(7×{10}^9\text{kg}\right)×\left(9.8\text{m}/{\text{s}}^2\right)×\left(36.5\text{m}\right)\\ & =& 2.50×{10}^{12}\text{J}\end{array}$

Therefore, the required gravitational potential stored in the Great Pyramid of Cheops is $2.50×{10}^{12}\text{J}$.

(b)

The energy contain of the daily food intake of an adult is,

$E_f=1.2×{10}^7\text{J}$

Comparing energies,

$\begin{array}{rcl}\frac{E_p}{E_f}& =& \frac{2.50×{10}^{12}\text{J}}{1.2×{10}^7\text{J}}\\ \frac{E_p}{E_f}& =& 208333.33\\ E_p& =& 208333.33\end{array}$

Therefore, the gravitational potential energy of the Great Pyramid of Cheops is 208333.33 times greater than the energy of food intake of an adult.