Question

hank has four objects with different masses. he measures the gravitational force between the objects when placed 1 m apart. which pair of masses will have the greatest gravitational force between them?
options: b and d, c and b, c and d, a and b
chart: table with columns \object\ (a, b, c, d) and \mass (kg)\ (15, 30, 50, 75)

Explanation:

The formula for gravitational force is \( F = G\frac{m_1m_2}{r^2} \). Since \( r = 1\space m \) (constant) and \( G \) is a constant, the force is proportional to the product of the masses (\( m_1 \times m_2 \)). We calculate the product for each pair:

Step1: Calculate product for B and D

\( m_B = 30\space kg \), \( m_D = 75\space kg \)
\( 30 \times 75 = 2250 \)

Step2: Calculate product for C and B

\( m_C = 50\space kg \), \( m_B = 30\space kg \)
\( 50 \times 30 = 1500 \)

Step3: Calculate product for C and D

\( m_C = 50\space kg \), \( m_D = 75\space kg \)
\( 50 \times 75 = 3750 \)

Step4: Calculate product for A and B

\( m_A = 15\space kg \), \( m_B = 30\space kg \)
\( 15 \times 30 = 450 \)

The largest product is for C and D, so they have the greatest gravitational force.

Answer:

C and D