The apparent weight of a man in a lift is `W_(1)` when lift moves upwards with some acceleration and is `W_(2)` when it is accerating down with same acceleration. Find the true weight of the man and acceleration of lift .

Explanation

(a) `W_(1)=m(g+a), W_(2)=m(g-a)`
`W_(1)+W_(2)=2mg rArr W_(1)+W_(2)=2W(because W=mg)`
`rArr (W_(1)+W_(2))/(2)=W`
(b) `(W_(1))/(W_(2))=(m(g+a))/(m(g-a))=(g+a)/(g-a)`
`(g)/(a)=(W_(1)+W_(2))/(W_(1)-W_(2)) rArr a=g((W_(1)-W_(2))/(W_(1)+W_(2)))`