It is a field force, the force with which a body is pulled towards the centre of the earth due to gravity. It has the magnitude mg, where m is the mass of the body and g is the acceleration due to gravity.

w = mg

1. Apparent Weight in a Lift

• When a lift is at rest or moving with a constant speed, then

                                                      R = mg

The weighing machine will read the actual weight.

                                                       V= 0

                                                   V = constant

                                      mg

• When a lift is accelerating upward, then apparent weight

                                  R₁ = m (g + a)

The weighing machine will read the apparent weight, which is more than the actual weight.

                                  mg

• When a lift is accelerating downward, then apparent weight

                                  R₂ = m (g – a)

The weighing machine will read the apparent weight, which is less than the actual weight.

                                               mg

• When lift is falling freely under gravity, then

                 R₂ = m (g – g) = 0

The apparent weight of the body becomes zero.

(v) If lift is accelerating downward with an acceleration greater than g, then body will lift from floor to the ceiling of the lift.

Rocket

Rocket is an example of variable mass following law of conservation of momentum.

Thrust on the rocket at any instant F = – u (dM / dt)

Where u = exhaust speed of the burnt and dM / dt = rate 0f gases combustion of fuel.

Velocity of rocket at any instant is given by u = V₀ + u log_e (M₀ / M)

Where, V₀ = initial velocity of the rocket,

M₀ = initial mass of the rocket and

M = present mass of the rocket.

If effect of gravity is taken into account then speed of rocket

u = V₀ + u log_e (M₀ / M) – gt