Question

A force of $12\text{N}$ produces an acceleration of $4{\text{m/s}}^2$ when it acts on a body $A$ and $6{\text{m/s}}^2$ when it acts on another body $B$. If the bodies $A$ and $B$ are tied together and a force of $10\text{N}$ is applied, what will be the acceleration?

• A. $1{\text{m/s}}^2$
• B. $2{\text{m/s}}^2$
• C. $3{\text{m/s}}^2$
• D. $4{\text{m/s}}^2$

Answer 1

The correct option is B $2{\text{m/s}}^2$

Let the mass of body $A$ and $B$ be $m_A$ and $m_B$ respectively.

Using, $F=ma$

For body $A:$

$12=m_A\times 4$

$\therefore m_A=3\text{kg}$

For body $B:$

$12=m_B\times 6$

$\therefore m_B=2\text{kg}$

When they are tied together, the combined mass, $m=m_A+m_B=5\text{kg}$

So, when a force of $10\text{N}$ acts on it,

$10=5\times a$

$\therefore a=2{\text{m/s}}^2$