Newton’s law of universal gravitation is represented by F = GmM r2 . where F is the magnitude of the gravitational force exerted by one small object on another, M and m are the masses of the objects, and r is a distance. Force has the SI units kg · m/s2. What is the SI units of the proportionality constant G? (a) kg · s2/m3 (b) m3/kg · s (c) m2/kg · s2 (d) kg2/m2 (e) m3/kg · s2 Q5: A solid piece of lead has a mass of 23.94 g and a volume of 2.10 cm3. From these data, what is the density of lead in SI units (in mega-gram per cubic meter)? (a) 1.14 M g/m3 (b) 1.14 × 104 M g/m3 (c) 11.4 M g/m3 3
Question
Newton’s law of universal gravitation is represented by F = GmM r2 . where F is the magnitude of the gravitational force exerted by one small object on another, M and m are the masses of the objects, and r is a distance. Force has the SI units kg · m/s2. What is the SI units of the proportionality constant G? (a) kg · s2/m3 (b) m3/kg · s (c) m2/kg · s2 (d) kg2/m2 (e) m3/kg · s2 Q5: A solid piece of lead has a mass of 23.94 g and a volume of 2.10 cm3. From these data, what is the density of lead in SI units (in mega-gram per cubic meter)? (a) 1.14 M g/m3 (b) 1.14 × 104 M g/m3 (c) 11.4 M g/m3 3
Solution
The first question is asking for the SI units of the gravitational constant, G. The formula for gravitational force is F = GmM/r^2. We know that the units for force (F) are kgm/s^2, the units for mass (m and M) are kg, and the units for distance (r) are m. We can rearrange the formula to solve for G: G = Fr^2/mM. Substituting the units in, we get G = (kgm/s^2)(m^2)/(kgkg), which simplifies to m^3/(kgs^2). Therefore, the SI units for G are m^3/(kgs^2), which corresponds to option (e).
The second question is asking for the density of lead in SI units given its mass and volume. The formula for density is mass/volume. The mass is given as 23.94 g, which is 0.02394 kg (since 1 kg = 1000 g). The volume is given as 2.10 cm^3, which is 2.1010^-6 m^3 (since 1 m = 100 cm). Therefore, the density is 0.02394 kg / 2.1010^-6 m^3 = 11.410^3 kg/m^3. However, the question asks for the answer in mega-grams per cubic meter. Since 1 kg = 0.001 Mg, the density is 11.410^3 * 0.001 Mg/m^3 = 11.4 Mg/m^3. Therefore, the answer is (c) 11.4 Mg/m^3.
Similar Questions
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