Net force determines acceleration under gravity and drag

Steps:

• Forces on each: downward weight $mg$, upward air resistance $R$.
• For X: net force $F_{net,X} = m_X g - R_X = m_X a_X$, so .
• For Y: $F_{net,Y} = m_Y g - R_Y = m_Y a_Y$, so .
• Given $m_Y = 2 m_X$ and $R_Y = 2 R_X$, then , so .

Why B is correct:

• Newton's second law shows $a = g - \frac{R}{m}$; equal $\frac{R}{m}$ ratios yield equal accelerations, which match but are less than twice (as , so but irrelevant here).

Why the others are wrong:

• A: Omits clarification that equality is less than twice, missing nuance against doubling misconception.
• C: Doubling ignores equal $R/m$ ratios preserving same $a$.
• D: Halving wrongly assumes acceleration scales inversely with mass alone.

Final answer: B