Question

A railway carriage box has its geometric centre (i.e we will assume the force due to gravity to act at this point) at a height of $1\text{m}$ above the rails, which are $1.5\text{m}$ apart. The maximum safe speed at which it could travel round an unbanked curve of radius $100\text{m}$ is

• A. $12m{s}^{-1}$
• B. $18m{s}^{-1}$
• C. $22m{s}^{-1}$
• D. $27.11m{s}^{-1}$

Answer 1

The correct option is D $27.11m{s}^{-1}$

Given that, $h=1\text{m},r=100\text{m},2x=1.5\text{m}$
For no skidding condition to satisfy, the component of normal reaction towards centre of circular curvature must provide the centripetal force & normal reaction's component in vertical direction must support the weight of carriage i.e $mg$
So, equation finally becomes:

$\frac{m{v}^2}{r}=\frac{mgx}{h}$
$v=\sqrt{\frac{grx}{1}}=\sqrt{\frac{9.8\times 100\times 0.75}{1}}$
$v=27.11m{s}^{-1}$