Question

Calculate the deflection due to Coriolis effect of a mass m dropped from a tower of height h at the north pole.

Answer 1

First the general formula for deflection in the northern hemisphere is calculated then it is applied to find the deflection in the north pole.

From point P the mass is dropped from height h along the vertical Z axis in the downward direction. Let XY plane be the horizontal plane with X directing east and Y north. The lattitude of the place be . Earth is rotating with angular velocity from west to east. lies in the YZ plane so has no component in the x direction. And let after a time t the velocity acquired by the mass be .

So,

So, the coriolis force acting on the body is,

As, in the northern hemisphere the velocity is downward so, v_z = - v.

So, the force on the mass is on the eastward direction. So, the displacement due to the Coriolis force also will be in the eastward direction.

So, now we use the fact that, v = gt, g = acceleration due to gravity.

, we get is by integrating the second step w.r.t dt.

Now, at t = 0, v = 0 = dx/dt. So, the constant(A) = 0.

Integrating again we get,

Now, at t = 0, x = 0 as at t = 0, v = 0, so no force and hence no deflection. i.e. the constant(B) = 0 also.

So, we get the deflection as,   and it is in the eastward direction() in the northern hemisphere.

Now, we have,

So, in terms of h we get the deflection as,

Now, in the north pole . Now, as cos(90) = 0. So, x= 0

So, we get no deflection in the northpole if any body of mass "m" is dropped from a tower of height "h".