Two bodies have masses in the ratio3:1. They experience forces which impart to them, acceleration in the ratio…

Analysis

To solve this problem, we need to use Newton’s Second Law of Motion, which relates force, mass, and acceleration. The formula is: $F = m \times a$ Where:

• $F$ = Force
• $m$ = Mass
• $a$ = Acceleration

Concept

When comparing two bodies, we can express the ratio of their forces as: $\frac{F_1}{F_2} = \frac{m_1 \times a_1}{m_2 \times a_2}$

We are given:

• Ratio of masses ($m_1 : m_2$) = $3 : 1$
• Ratio of accelerations ($a_1 : a_2$) = $2 : 9$

Step-by-Step Solution

1. Set up the ratio formula: $\frac{F_1}{F_2} = \left( \frac{m_1}{m_2} \right) \times \left( \frac{a_1}{a_2} \right)$

2. Substitute the given values: $\frac{F_1}{F_2} = \left( \frac{3}{1} \right) \times \left( \frac{2}{9} \right)$

3. Perform the multiplication: $\frac{F_1}{F_2} = \frac{3 \times 2}{1 \times 9}$ $\frac{F_1}{F_2} = \frac{6}{9}$

4. Simplify the fraction: Divide both the numerator and the denominator by their greatest common divisor, which is 3: $\frac{6 \div 3}{9 \div 3} = \frac{2}{3}$

The ratio of the forces is 2:3.

Conclusion

Comparing our result to the options provided, we see that it matches option C.

Exam Tip: When dealing with ratio problems in Physics, always write down the formula first and group the ratios together. It prevents simple arithmetic errors and keeps your work organized. Don't let the "respectively" in the question confuse you—it simply means the first value in the mass ratio corresponds to the first value in the acceleration ratio.