When a vehicle of mass $m$ is moving with a velocity $v$ over a concave over-bridge of radius of curvature…

When a vehicle of mass $m$ is moving with a velocity $v$ over a concave over-bridge of radius of curvature $r$, the thrust on the road at the lowest point on the bridge will be
  1. $m g+\frac{m v^2}{r}$
  2. $m g-\frac{m v^2}{r}$
  3. $\frac{m^2 v^2 g}{r}$
  4. $\frac{v^2 g}{r}$

Solution

Let the mass of the vehicle be $m$ and velocity of the vehicle be $v$, the radius of curvature of over-bridge be $r$. The centripetal force on the vehicle $=\frac{m v^2}{r}$ The thrust on the road at lowest point, $F_{\text {Net }}=$ weight of the vehicle + centripetal force $ =m g+\frac{m v^2}{r} $

Asked in: AP EAMCET 2021 (25 Aug Shift 1)

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