Question

why should a passenger tend to fail sideways when the bus takes a sharp u turn

Answer 1

When the bus turns, it can only influence the passenger through the point of contact between the bus and the person. For clarity, let us assume a standing passenger.

So, if the bus turns  left, the feet move left following the floor (due to frictional contact between the bus and the feet; that is the feet experience a force to the left. But the force acts on the feet, not though the centre of mass of the body higher in the torso.

And any such off centre force creates a torque about the centre of mass, so if your feet go left, your head must spin right (i.e. "outward" with respect to the bus.) To prove this put a pencil on a smooth surface and flick one end with your finger - it spins about its centre with the "head" going the opposite way to the direction you you flick the "foot".

BTW if you lean left just far enough so that the torque on your body due to your feet, is just balanced by the torque around your feet due to gravity, then you can go around the corner without hanging on to anything (Hoping like heck the driver does not brake or swerve suddenly)

Lots of fun to do this on trains and buses, but fair warning: you could be injured, and you look like a complete idiot when you get it wrong!

Answer 2

our body will be in the state of rest and as soon as the bus takes a sharp turn the body changes it's state of rest to the state of motion that is why a person tends to fall sideways when the bus takes a sharp turn