Mass, Weight and Density — Solutions
Full worked solutions, with method and final answer for every part.
Question 1
(a)Mass is the amount of matter in an object (in kg) and does not change with location; weight is the force of gravity on that mass (in N) and depends on the local gravitational field strength.
Mass = constant amount of matter; weight = gravitational force, varies with g
(b)W = mg.
W = 60 × 10 = 600 N
(c)W = mg using the Moon's g.
W = 60 × 1.6 = 96 N
Question 2
(a)Density = mass ÷ volume.
ρ = 270 ÷ 100 = 2.7 g/cm³
(b)An object floats if its density is less than that of the liquid it is in.
Its density is less than 1.0 g/cm³
Question 3
(a)Mass = density × volume.
m = 8.0 × 50 = 400 g
(b)Reshaping doesn't add or remove material, so mass is unchanged. Density = mass/volume also stays the same, since both mass and total volume of material are unchanged (only the shape changes).
Mass unchanged; density unchanged
Question 4
(a)W = mg.
15 × 10 = 150 N
Question 5
(a)Density = mass ÷ volume.
200 ÷ 80 = 2.5 g/cm³
Question 6
(a)Mass = density × volume.
2.7 × 40 = 108 g
Question 7
(a)Volume = mass ÷ density.
500 ÷ 8.0 = 62.5 cm³
Question 8
(a)W = mg, using Jupiter's g.
10 × 25 = 250 N
Question 9
(a)Mass depends only on the amount of matter in the object, which doesn't change with location. Weight depends on the local gravitational field strength, which is weaker on the Moon (about 1/6 of Earth's), so weight decreases even though mass is unchanged.
Mass is unchanged (same amount of matter); weight decreases because the Moon's gravitational field strength is weaker
Question 10
(a)Density = mass ÷ volume. With equal mass, a smaller volume gives a larger density.
The block with the smaller volume has the greater density
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