A particle of mass $m=0.5\text{ kg}$ is moving in a circle of radius $r=2\text{ m}$ with a constant speed of $v=4\text{ m/s}$. What is the net force $F$ acting on the particle?

Solution

1. Identify the given values: mass $m=0.5\text{ kg}$, radius $r=2\text{ m}$, and speed $v=4\text{ m/s}$.
2. Use the formula for centripetal force: $F=\frac{m{v}^2}{r}$.
3. Substitute the values into the equation: $F=\frac{0.5\times 4^2}{2}$.
4. Simplify the expression: $$\begin{array}{rl}F& =\frac{0.5\times 16}{2}\\ & =\frac{8}{2}\\ & =4\text{ N}\end{array}$$.
5. Hence the answer is (B).