Question

A force produces an acceleration of $5\raisebox{1ex}{$cm$}\!\left/ \!\raisebox{-1ex}{$s^2$}\right.$. When it acts on a body of $20g$. Then the force in newtons is:

• A. ${10}^{-4}N$
• B. ${10}^{-2}N$
• C. ${10}^{-3}N$
• D. ${10}^{5}N$

Answer 1

The correct option is C

${10}^{-3}N$

Step 1: Given data

$$\begin{gathered} a=5\raisebox{1ex}{$cm$}\!\left/ \!\raisebox{-1ex}{$s^2$}\right. \\ m=20g \end{gathered}$$

Step 2: Formula used

$$\begin{gathered} F=m\times a \\ F\to Force \\ m\to mass \\ a\to acceleration \end{gathered}$$

Step 3: The calculation for acceleration and mass in SI units

$$\begin{gathered} 1m=100cm \\ 1Kg=1000g \\ a=5\raisebox{1ex}{$cm$}\!\left/ \!\raisebox{-1ex}{$s^2={\displaystyle \frac{5}{100}}=0.05{\displaystyle \raisebox{1ex}{$m$}\!\left/ \!\raisebox{-1ex}{$s^2$}\right.}$}\right. \\ m=20g=\frac{20}{1000}=0.02Kg \end{gathered}$$

Step 4: The calculation for the force

$$\begin{gathered} F=0.02\times 0.05 \\ F=10\times {10}^{-4} \\ F={10}^{-3}N \end{gathered}$$

Hence, option C is correct.