Question

What is the maximum speed at which a railway carriage can move without toppling over along a curve of radius $R=200m$ if the distance from the centre of gravity of the carriage to the level of the rails is $h=1.0m$, the distance between the rails is $h=1.0m$, the distance between the rails is $l=2.0m$ and the rails are laid horizontally? (Take $g=10m/s^2$)

• A. $11.18m{s}^{-1}$
• B. $22.36m{s}^{-1}$
• C. $44.72m{s}^{-1}$
• D. $74m{s}^{-1}$

Answer 1

The correct option is C $44.72m{s}^{-1}$

In railway carriage's frame, the carriage is in translational as well as rotational equilibrium.

Rotational equilibrium : Torque about point O is zero i.e ${\tau }_o=0$

$\therefore$ $f\times 1-N\times 1=0$ $⟹f=N$

Translational equilibrium :

$\therefore$ $mg=N$ $⟹mg=f$ ..........(1)

Also $f=m{a}_r$ .........(2)

From (1) and (2), we get $m{a}_r=mg$

$\therefore$ $\frac{m{v}^2}{r}=mg$ $⟹v=\sqrt{rg}$

$\therefore$ $v=\sqrt{200\times 10}=44.72$ $m/s$