Q. A man is standing in a lift which goes up and comes down with the same constant acceleration. If the ratio of the apparent weights in the two cases is $2: 1$, then the acceleration of the lift is : (Take $g=10 \,m / s ^{2}$ )

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A

$3.33 \,ms ^{-2}$

B

$2.50 \, ms ^{-2}$

C

$2.00 \, ms ^{-2}$

D

$1.67 \,ms ^{-2}$

Solution:

When lift goes upwards with constant acceleration $a$,
$W_{1}=m(g+a)\,\,\,$...(1)
When lift goes downwards with constant acceleration $a$,
$W_{2}=m(g-a)\,\,\,$...(2)
$ \frac{W_{1}}{W_{2}} =\frac{m(g+a)}{m(g-a)}=\frac{2}{1} $
$ g+a =2 g-2 a $
$ 3 a =g $
$a =\frac{g}{3}=\frac{10}{3}=3.33 \,m / s ^{2} $

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