Answer
(a) The acceleration due to gravity on the surface of Venus is
$8.87~m/s^2$.
(b) The weight of the rock on the surface of Venus is 67.9 N.
Work Step by Step
(a) Let $M$ be the mass of the earth.
Let $R$ be the radius of the earth.
We can write an expression for the acceleration due to gravity on the earth's surface.
$\frac{G~M}{R^2} = 9.80~m/s^2$
We can find the acceleration due to gravity on Venus.
$\frac{(G)(0.815~M)}{(0.949~R)^2} = \frac{0.815}{(0.949)^2}~(9.80~m/s^2)$
$\frac{(G)(0.815~M)}{(0.949~R)^2} = 8.87~m/s^2$
The acceleration due to gravity on the surface of Venus is
$8.87~m/s^2$.
(b) We can find the mass of the rock.
$m = \frac{75.0~N}{9.80~m/s^2}$
$m = 7.65~kg$
We can find the weight of the rock on the surface of Venus.
$weight = (7.65~kg)(8.87~m/s^2)$
$weight = 67.9~N$
The weight of the rock on the surface of Venus is 67.9 N.
