Question

A force $F$ is acting on an object of mass $m$ to give it an acceleration of $a$ . If $m$ is halved and $F$ is quadrupled, what happens to $a$ ?

• A. It is divided by eight
• B. It is divided by two
• C. It remains unchanged
• D. It is multiplied by two
• E. It is multiplied by eight

Answer 1

The correct option is E It is multiplied by eight

Newtons Second Law tells us that $F=ma$ . From this we can infer that $a=\frac{F}{m}$ . Since $F$ is directly proportional to $a$ , quadrupling $F$ will also quadruple $a$ . And since $m$ is inversely proportional to $a$ , halving $m$ will double $a$ . Were quadrupling $a$ and then doubling $a$ , which means that, ultimately, multiplying $a$ by eight.