Question

If the forces acting on two bodies of masses \(2kg\) and \(3kg\) are same, then the ratio of their respective accelerations is

• A. 1:1
• B. 1:2
• C. 2:3
• D. 3:2
• E. 4:9

Hint:

For a constant force, acceleration is inversely proportional to mass.

Answer 1

The Correct Option is D

Step 1: Understanding the Concept:
This problem applies Newton's Second Law of Motion, which relates force (F), mass (m), and acceleration (a).
Step 2: Key Formula or Approach:
Newton's Second Law is given by the formula: \[ F = ma \] We are given information about two bodies, let's denote them by subscripts 1 and 2.
\(m_1 = 2\) kg
\(m_2 = 3\) kg
We are told that the forces acting on them are the same: \[ F_1 = F_2 \] Step 3: Detailed Explanation:
Using Newton's Second Law for each body: \[ F_1 = m_1 a_1 \] \[ F_2 = m_2 a_2 \] Since \(F_1 = F_2\), we can set the expressions equal to each other: \[ m_1 a_1 = m_2 a_2 \] We need to find the ratio of their respective accelerations, which is \(a_1 : a_2\) or \( \frac{a_1}{a_2} \). To get this ratio, we rearrange the equation: \[ \frac{a_1}{a_2} = \frac{m_2}{m_1} \] Now, substitute the given masses: \[ \frac{a_1}{a_2} = \frac{3 \text{ kg}}{2 \text{ kg}} = \frac{3}{2} \] So, the ratio of their accelerations is 3 : 2.
Step 4: Final Answer:
The ratio of the respective accelerations (\(a_1 : a_2\)) is 3 : 2. This corresponds to option (D).