Question

A car of mass $1000\text{kg}$ moves in a circular path with a constant speed of $16\text{m/s}$. It is turned by ${90}^{\circ }$, while travelling a distance of $628\text{m}$ on the road. The centripetal force acting on the car is

• A. $160\text{N}$
• B. $320\text{N}$
• C. $1280\text{N}$
• D. $640\text{N}$

Answer 1

The correct option is D $640\text{N}$

Given, mass of car $\left(m\right)=1000\text{kg}$
Speed of car $\left(v\right)=16\text{m/s}$
To find centripetal force:
$F_c=\frac{m{v}^2}{r}$

We need to find ${}^{\prime }{r}^{\prime }$

To find $r:$ Given that car has turned ${90}^{\circ }$ after travelling $628\text{m}$, distance covered for quarter circle is,

$\Rightarrow \frac{\pi r}{2}=628\Rightarrow r=400\text{m}$ $(\pi =3.14)$

Hence the centripetal force will be,
$F_c=\frac{1000\times (16{)}^2}{400}=640\text{N}$

Option D is the correct answer