Question

A certain force applied to a body A gives it an acceleration of $10m{s}^{-2}$. The same force applied to body B gives it an acceleration of $15m{s}^{-2}$. If the two bodies are joined together and the same force is applied to the combination, the acceleration will be:

• A. $6m{s}^{-2}$
• B. $25m{s}^{-2}$
• C. $12.5m{s}^{-2}$
• D. $9m{s}^{-2}$

Answer 1

The correct option is A $6m{s}^{-2}$

Given,

Acceleration of mass $M_1$ (when force $F$ applied) $a_1=10m/s^2$

Acceleration of mass $M_2$ (when force $F$ applied) $a_2=15m/s^2$

$M_1=\frac{F}{a_1}=\frac{F}{10}\&M_2=\frac{F}{a_2}=\frac{F}{15}$

When both masses are combined

For combine mass $M_{total}=M_1+M_2$ , Force $=F$ & acceleration $a_{total}$

$F=M_{total}{a}_{total}$

$F=(\frac{F}{10}+\frac{F}{15})a_{total}=\frac{F{a}_{total}}{6}$

$a_{total}=6m/s^2$

Combine mass acceleration is $6m/s^2$