Question

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

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

Answer 1

The correct option is C $500\sqrt{2}\text{N}$

Given tangential acceleration $a_t=1{\text{ms}}^{-2}$
Tangential force $\Rightarrow m{a}_t=500\left(1\right)=500\text{N}$
Given $D=50m\Rightarrow R=25m$
Centripetal acceleration
$a_C=\frac{v^2}{R}=\frac{25}{25}=1$
Centripetal force
$\Rightarrow m{a}_C=500\left(1\right)$


$F=\sqrt{(m{a}_t{)}^2+(m{a}_C{)}^2}$
$=\sqrt{{500}^2+{500}^2}$
$=500\sqrt{2}\text{N}$