The mass of Venus is 81.5% that of the earth, and its radius is 94.9% that of the earth. (a) Compute the acceleration due to gravity on the surface of Venus from these data. (b) If a rock weighs 75.0 N on earth, what would it weigh at the surface of Venus?

Problem 12E Solution 12 E Step 1 : Introduction In this question, we need to find the acceleration due to gravity on the surface of Venus In this second part we need to find the weight of rock on surface on Venus Data given Mass of Venus 81.5 % of the Earth = 0.815 g of earth Radius of Venus 94.9% of the Earth Mass of rock on surface of Earth m = 75.0 N Step 2 : To find the acceleration due to gravity on the surface of Venus We know gravitational force on earth is g e 9.8 m/s 2 By inverse square law we have Radius of venus as 2 1/r = 1/0.949 2 1/r = 1.11 m Hence the radius of venus is 1.11 m of the earth From this we can obtain gravitational force on Venus as gV = (M v )vg e Substituting values we get g = (0.815 g × 1.11 m ) g V e g = 0.904 × 9.8 m/s 2 V g = 8.865 m/s 2 V 2 This can be approximated as g V = 8.88 m/s 2 Hence we have gravitational force on Venus as 8.88 m/s