Question

A force of 5 N gives a mass \(M_1\) an acceleration equal to \(8 \, \text{m/s}^2\) and \(M_2\) an acceleration equal to \(24 \, \text{m/s}^2\). What is the acceleration, if both masses are tied together?

• A. \(16 \, \text{m/s}^2\)
• B. \(6 \, \text{m/s}^2\)
• C. \(12 \, \text{m/s}^2\)
• D. \(4 \, \text{m/s}^2\)

Hint:

When same force acts separately, find masses first, then combine and apply Newton’s law again.

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
Force, mass, and acceleration are related by \( F = ma \). When masses are tied together, the total mass is the sum of individual masses, and they experience a common acceleration under the same force.
: Key Formula or Approach:
1. Find individual masses: \( m = F/a \).
2. Total mass \( M = M_1 + M_2 \).
3. Combined acceleration \( a_{net} = F/M \).
Step 2: Detailed Explanation:
Given \( F = 5 \text{ N} \).
For mass \( M_1 \): \( M_1 = \frac{F}{a_1} = \frac{5}{8} \text{ kg} \).
For mass \( M_2 \): \( M_2 = \frac{F}{a_2} = \frac{5}{24} \text{ kg} \).
When tied together, total mass \( M \):
\[ M = M_1 + M_2 = \frac{5}{8} + \frac{5}{24} \]
Find LCM (24):
\[ M = \frac{15 + 5}{24} = \frac{20}{24} = \frac{5}{6} \text{ kg} \]
Now, combined acceleration \( a \):
\[ a = \frac{F}{M} = \frac{5}{5/6} = 5 \times \frac{6}{5} = 6 \text{ m/s}^2 \]
Step 3: Final Answer:
The acceleration when tied together is \( 6 \text{ m/s}^2 \).