Question

An object of $60\text{kg-wt}$ is weighed by hanging it to the spring balance, from the ceiling of a car. If the car starts moving around a curve of radius $10\text{m}$ at a speed $10{\text{ms}}^{-1}$. The reading of the spring balance would be

• A. $60\sqrt{2}\text{kg-wt}$
• B. $60\text{kg-wt}$
• C. $120\sqrt{2}\text{kg-wt}$
• D. $600\text{kg-wt}$

Answer 1

The correct option is A $60\sqrt{2}\text{kg-wt}$

Here, $r=10\text{m},v=10{\text{ms}}^{-1},m=60\text{kg}$

Reading of the spring balance= resultant force $=?$

We know that , two forces are acting as weight $\left(mg\right)$ and centripetal force,
$\left(\frac{m{v}^2}{r}\right)$ are at ${90}^{\circ }$ to each other.

$\therefore$ Resultant force $=\sqrt{(mg{)}^2+{\left(\frac{m{v}^2}{r}\right)}^2}=mg{[1+{\left(\frac{v^2}{rg}\right)}^2]}^{1/2}$
$=60\times 10{[1+{\left(\frac{10\times 10}{10\times 10}\right)}^2]}^{1/2}$

$=(60\times 10\times \sqrt{2})\text{N}=60\sqrt{2}\text{kg-wt}$

Hence option A is the correct answer.