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

Concept: From Newton’s second law: \[ F = ma \Rightarrow m = \frac{F}{a} \]

Step 1: Find masses.
\[ M_1 = \frac{5}{8}, \quad M_2 = \frac{5}{24} \]

Step 2: Total mass.
\[ M = \frac{5}{8} + \frac{5}{24} = \frac{15 + 5}{24} = \frac{20}{24} = \frac{5}{6} \]

Step 3: Acceleration of system.
\[ a = \frac{F}{M} = \frac{5}{5/6} = 6 \, \text{m/s}^2 \]