We feel our weight from the normal reaction force (N) that we receive from the surface. Weightlessness is a situation in which the apparent weight is zero due to absence of normal reaction force ( \(N = 0\) ) [ surface does not exert any force on the body ]. The following are the conditions for feeling weightless.
(A) When no real Gravitational Force is acting and you are in a non - accelerated frame of reference.
1)If you are at a infinite distance from the celestial objects, then your weight will be zero. (Example if you are at a infinite distance from Earth). From the universal law of gravitation \(F = \frac{Gm_1m_2}{r^2}\) we get F is inversely proportional to \(r^2\). So, F becomes zero when r is infinity.
2) If you are present in neutral gravitational point between two planets. Consider two celestial objects of mass M and m seperated by a distance d. There exists a point at a distance \[x = \frac{d}{1+\sqrt{\frac{m}{M}}}\] from mass M such that the net gravitational force is zero.
3) If you are the centre of a celestial object( example if you are at the centre of earth ). When we go inside spherical celestial objects we cannot assume its entire mass to be concentrated at the centre. According to our position we have to imagine a sphere of radius equal to our distance from the centre. The mass can be calculated by assuming the density to be constant. At the centre , the radius of the assumed sphere will be zero and hence its mass will also be zero. Due to this gravitational force will be zero.
(B) When real gravitational force is acting
i) When you are in non - Accelerated Frame of Reference
1) If you are in fluid medium of density more than or equal to your density. Fluids exert buoyant force on the submerged object whose direction is opposite to the gravitational force. When the density of the fluid is equal to the density of the object, the buoyant force equals the gravitational force and hence net force is zero.
ii) When you are in Accelerated Frame of Reference
1) If you are in a lift [or any object ] that is accelerating downwards with an acceleration equal to acceleration due to gravity. Pseudo force of magnitude mg acts in the direction opposite to the gravitational force. This exactly balances the weight of the body.
2) If you jump off the building , then while you are in air, you will feel almost weightless [ Free Fall ]. Pseudo force of magnitude mg acts in the direction opposite to the gravitational force. This exactly balances the weight of the body. In other words, since there is no contact with any surface, normal contact force is zero which makes us feel weightless.
3) In space satellites , astronauts feel weightless. Satellites are launched so as to establish it in the desired orbit with the correct speed. Centrifugal force acts away from the centre of the Earth. This force exactly balances the weight of the body.
4) If the time period of rotation of the Earth becomes 84.6min, we will feel weightless on Equator. Due to the axial rotation of the Earth, we experience a pseudo force. This reduces the effective weight.
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