Question

A certain force applied to a body A gives it is acceleration of $10$ $m{s}^{-2}$. The same force applied to body B gives it an acceleration of $15$ $m{s}^{-2}$. 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 $6m{s}^{-2}$

We know force = mass$\times$acceleration

Condition force applied on bodies is $F_A=F_B=F$

Thus $F_A=m_A{a}_A$ and $F_B=m_B{a}_B$

From condition we can conclude that

$m_A{a}_A=m_B{a}_B$

$\frac{m_A}{m_B}=\frac{a_B}{a_A}=\frac{15}{10}{m}_A=1.5m_B$

Now as same amount of force F is applied when both the bodies are combined together we get

$F=(m_A+m_B)\times a_C$

Also we know force $F=m_B{a}_B$

Therefore

$m_B{a}_B=(m_A+m_B)a_c$

$15m_B=2.5m_B{a}_c$

$a_c=6m/s^2$