Answer:
K = G Mm / 9R
Explanation:
Expression for escape velocity V_e =
Kinetic energy at the surface = 1/2 m V_e ²
= 1/2 x m x 2GM/R
GMm/R
Potential energy at the surface
= - GMm/R
Total energy = 0
At height 9R ( 8R from the surface )
potential energy
= - G Mm / 9R
Kinetic energy = K
Total energy will be zero according to law of conservation of mechanical energy
so
K - G Mm / 9R = 0
K = G Mm / 9R
Answer: a. m = 7.7 kg
b. V = 435.52 in³
c. m = 1927 kg
d. V = 335.37 cm³
e. m = 3 kg
Explanation: <u>Density</u> is the ratio of mass per volume, i.e., it's the measure of an object's compactness. Its representation is the greek letter ρ.
The formula for density is
Density's unit in SI is kg/m³, but it can assume lots of other units.
Some unit transformations necessary for the resolution of the question:
1 L = 1 dm³ = 1000 cm³
1 in³ = 16.3871 cm³
1 g = 0.001 kg
a. V = 1.34 L = 1340 cm³
m = 5.75 * 1340
m = 7705 g => 7.705 kg
Mass of object 1 with volume 1.34L is 7.7 kg.
b. A cube's volume is calculated as V = side³
V = 7.58³
V = 435.52 in³
Volume of object 2 is 435.52 in³.
c. Using 1 in³ = 16.3871 cm³ to change units:
V = 435.52 * 16.3871
V = 713689.4 cm³
Then, mass will be
m = 2.7 * 713689.4
m = 1926961.4 g => 1927 kg
Mass of object 2 is 1927 kg.
d. Volume of a sphere is calculated as
Diameter is twice the radius, then r = 4.31 cm.
Volume is
V = 335.37 cm³
Volume of object 3 is 335.37 cm³.
e.
m = 8.96 * 335.37
m = 3004.91 g => 3 kg
Mass of object 3 is 3 kg.