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What is the mass of 0.25L of the substance in grams? The density of a substance is 1.63 g/mL.

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A

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Part 7· 3 steps

The weight of an object is the gravitational force acting on it. According to Newton's Law of Universal Gravitation, the force of gravity is inversely proportional to the square of the distance from the center of the Earth.
Let W1W_1 be the weight on Earth's surface and RER_E be the Earth's radius. The distance from the center of the Earth is r1=REr_1 = R_E.
When the object is moved one Earth radius above the surface, the new distance from the center of the Earth is r2=RE+RE=2REr_2 = R_E + R_E = 2R_E.

  1. State the initial weight and distances.

    Initial weight W1=100 NW_1 = 100 \text{ N} at distance r1=REr_1 = R_E.
    New distance r2=2REr_2 = 2R_E.

  2. Apply the inverse square law for gravitational force.

    The new weight W2W_2 is related to the initial weight W1W_1 by the ratio of the square of the distances:

    W2=W1(r1r2)2W_2 = W_1 \left( \frac{r_1}{r_2} \right)^2

  3. Substitute the values and calculate the new weight.

    W2=100 N(RE2RE)2W_2 = 100 \text{ N} \left( \frac{R_E}{2R_E} \right)^2 W2=100 N(12)2W_2 = 100 \text{ N} \left( \frac{1}{2} \right)^2 W2=100 N×14W_2 = 100 \text{ N} \times \frac{1}{4} W2=25 NW_2 = 25 \text{ N}

    The correct option is A.

    • A. 25N

Part 8· 4 steps

The relationship between density, mass, and volume is given by the formula:

Density=MassVolume\text{Density} = \frac{\text{Mass}}{\text{Volume}}

To find the mass, we can rearrange the formula:

Mass=Density×Volume\text{Mass} = \text{Density} \times \text{Volume}

  1. Identify the given density and volume.

    Density =1.63 g/mL= 1.63 \text{ g/mL}.
    Volume =0.25 L= 0.25 \text{ L}.

  2. Convert the volume from liters (L) to milliliters (mL) to match the units of density.

    We know that 1 L=1000 mL1 \text{ L} = 1000 \text{ mL}.

    Volume in mL=0.25 L×1000 mL1 L=250 mL\text{Volume in mL} = 0.25 \text{ L} \times \frac{1000 \text{ mL}}{1 \text{ L}} = 250 \text{ mL}

  3. Calculate the mass using the formula.

    Mass=1.63gmL×250 mL\text{Mass} = 1.63 \frac{\text{g}}{\text{mL}} \times 250 \text{ mL}

  4. Perform the multiplication.

    Mass=407.5 g\text{Mass} = 407.5 \text{ g}

    The correct option is C.

    • C. 407.5g
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