A train is moving with a speed of 12text m/s$12\text{ m/s}$ on rails which are 1.5text m$1.5\text{ m}$ apart. To negotiate a curve of radius 400text m$400\text{ m}$, the height by which the outer rail should be raised with respect to the inner rail is (Given, g = 10text m/s^2$g = 10\text{ m/s}^{2}$):

### Related Formula f_s leq mu_s N$$f_s \leq \mu_s N$$ F_c = mromega^2$$F_c = mr\omega^2$$ ### Core Logic

To prevent the coin from slipping, the static friction must provide the necessary centripetal force for circular motion. f = momega^2 r$f = m\omega^2 r$ The normal force on the flat disc is N = mg$N = mg$. The maximum static friction is f_textmax = mu N = mu mg$f_{\text{max}} = \mu N = \mu mg$. For no slipping: m r omega^2 leq mu mg$$m r \omega^2 \leq \mu mg$$ omega^2 leq fracmu gr$$\omega^2 \leq \frac{\mu g}{r}$$ omega_textmax = sqrtfracmu gr$$\omega_{\text{max}} = \sqrt{\frac{\mu g}{r}}$$ ### Evaluation Rubric / Model Answer null ### Chapter Mix Class 11 Physics: Laws Of Motion