Non swinging pendulum hanging from ceiling of airplane going

Solution

Initially it has Ke , since it is moving along with the plane.

Ke_non-swing= 1/2mv_i²= 1/2*m* 222.2²= 111.1 m J

Pe_non-swing= mgh= mgR_e= m*9.8* 6.4*10⁶ = 62.7*10⁶ mJ [ R_e- radius of earth =6.4*10⁶m]

Now , when it swings it\'s potential energy with angular deviation is

Pe_swing = mgR_e[1-costheta]= m*62.7*10⁶[1-cos theta]

Ke_swing=0 J

So Total energy before swing and after remains constant [ Conservation of energy]

Ke_non-swing +Pe_non-swing =Ke_swing +Pe_swing

111.1 m J +62.7*10⁶ mJ   = 0J +m*62.7*10⁶[1-cos theta]

[1-cos theta]= 0.999

theta= 90.0 ^o

Angular deviation of the string of the pendulum relative to a line to the center of the earth is 90 degrees