A man in a lift feels an apparent weight W when the lift is moving up with a uniform acceleration of 1/3rd of the acceleration due to gravity. If the same man were in the same lift now moving down with a uniform acceleration that is 1/2 of the acceleration due to gravity, then his apparent weight is

Explanation

Case (i) : When lift is moving upwards :
Apparent weight of the man = W
Acceleration , a = `g//3`
Apparent weight of the man when the lift is moving upwards is ,
`W=m(a+g)=m((g)/(3)+g)`
`= (4)/(3)mg=(4)/(3)N" " [becauseN=mg`
`rArrN=(3)/(4)W`
Case (ii) : When lift is moving downwards :
Let W ' be the apparent weight of the man Acceleration , a = g / 2
Apparent weight of the man when the lift is moving downwards is ,
`W'=m(g-a)=m(g-g//2)`
`=(1)/(2)mg=(N)/(2) [becauseN = mg] `
`=(1)/(2)((3)/(4)W)=(3)/(8)W`