91Ó°ÊÓ

• The mass of Venus is to 81.5% that of mass of Earth.
• The radius of Venus is 94.9% that of Earth.
• The weight of the rock is W_E=75.0 N

Part (a)

The mass of Venus M_v is 81.5% that of mass of Earth and it can be expressed as,

$M_v=0.815\text{ }{M}_E$

Here, M_E is the mass of Earth.

The radius of Venus R_V is 94.9% that of earth and it can be expressed as,

$R_V=0.949R_E$

Here, R_E is the radius of Earth.

The acceleration due to gravity on the surface of Venus can be expressed as,

$g_V=\frac{G{M}_V}{{R_V}^2}$

Substitute $0.815\text{ }{M}_E$ for M_v , $0.949R_E$ for R_V in the above equation,

$\begin{array}{c}{g}_V=\frac{G\left(0.815M_E\right)}{{\left(0.949R_E\right)}^2}\\ =0.905\frac{G{M}_E}{{R_E}^2}\\ =0.905×g_{earth}\end{array}$

The acceleration due to gravity on the surface of Venus can be calculated as,

$\begin{array}{c}{g}_V=0.905×9.8\text{″¾}/{\text{s}}^{\text{2}}\\ =8.87\text{″¾}/{\text{s}}^{\text{2}}\end{array}$

Thus, the acceleration due to gravity on the surface of Venus is 8.87 m/s².

Part (b)

The weight of the rock is on earth is 75.0 N and it is expressed as,

$\begin{array}{c}{W}_E=m{g}_E\\ 75.0\text{ N}=m{g}_E\end{array}$

Here, m is the mass of the rock, and g is the acceleration due to gravity on the surface of Earth.

Hence, the mass of the rock can be expressed as,

$m=\frac{W_E}{g_E}$

The acceleration due to gravity on the surface of the Venus can be expressed as,

$g_V=\left(0.905×g_E\right)$

Here, g_E is the acceleration due to gravity on the surface of earth.

The weight of the rock at the surface of Venus can be expressed as,

$W_V=m{g}_V$

Substitute the values in the above equation,

$\begin{array}{c}{W}_V=\frac{W_E}{g_E}\left(0.905×g_E\right)\\ =\left(0.905×W_E\right)\\ =\left(0.905×75.0\text{ N}\right)\\ =67.9\text{ N}\end{array}$

Thus, the weight of the rock at the surface of Venus is 67.9 N.