Question

A car is moving on a circular road of diameter $50\, m$ with a speed of $5m\, s^{-1}$. It is suddenly accelerated at a rate of $1 \,ms^{-2}$. If the mas s of the car is $500 \,kg$, then the net force acting on the car is

• A. $5\,N$
• B. $1000\,N$
• C. $500\sqrt{2}\,N$
• D. $\frac{500}{\sqrt{2}}\,N$

Answer 1

Answer: (C)

$500\sqrt{2}\,N$

Answer 2

Here, $r= 25\, m, v= 5\, m \,s^{-1}, m= 500\, kg$ $a_{t} = 1\, m\,s^{-2}, a_{r} = \frac{v^{2}}{r} = \frac{5\times 5}{25} = 1\, m\,s^{-2}$ $a_{\text{net}} = \sqrt{a_{r}^{2} +a_{t}^{2}} = \sqrt{1^{2}+1^{2}} = \sqrt{2}\, m\, s^{-2}$ $F = ma_{\text{net} } = 500\sqrt{2}N$