Q. A railway carriage has its centre of gravity at a height of 1 m above the rails, which are 1.5 m apart. The maximum safe speed at which it could travel round an unbanked curve of radius 100 m is
A) $12\ ms^{- 1}$
B) 18$\ ms^{- 1}$
C) 22$\ ms^{- 1}$
D) 27 $ms^{- 1}$
Explanation
(d) Here, $h = 1\ m,r = 100\ m,2x = 1.5\ m$
For no skidding
$\frac{mv^{2}}{r} \times h = mg\ x$
$v = \sqrt{\frac{g\ r\ x}{h}} = \sqrt{\frac{9.8 \times 100 \times 0.75}{1}}$
$v = 27.1\ ms^{- 1}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.