Question

A constant force acts on two different masses independently and produces accelerations \( A_1 \) and \( A_2 \). When the same force acts on their combined mass, the acceleration produced is

• A. \( A_1 - A_2 \)
• B. \( A_1 + A_2 \)
• C. \( \frac{A_1 A_2}{A_1 + A_2} \)
• D. \( \sqrt{A_1^2 + A_2^2} \)

Hint:

Acceleration of combined masses under the same force follows the "parallel resistor" formula style.

Answer 1

The Correct Option is C

Step 1: Newton's Second Law
$F = m_1 A_1 \implies m_1 = \frac{F}{A_1}$.
$F = m_2 A_2 \implies m_2 = \frac{F}{A_2}$.
Step 2: Combined Mass
For combined mass $M = m_1 + m_2$, the acceleration $A$ is:
$A = \frac{F}{m_1 + m_2}$.
Step 3: Calculation
$A = \frac{F}{\frac{F}{A_1} + \frac{F}{A_2}} = \frac{1}{\frac{A_2 + A_1}{A_1 A_2}} = \frac{A_1 A_2}{A_1 + A_2}$.
Final Answer: (C)