Explanation:
When lift goes upwards with constant acceleration \(a\)
\({W_1} = m(g + a)\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,(1)\)
When lift goes downwards with constant acceleration \(a\)
\({W_2} = m(g - a)\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,(2)\)
\(\frac{{{W_1}}}{{{W_2}}} = \frac{{m(g + a)}}{{m(g - a)}} = \frac{2}{1}\)
\(g + a = 2g - 2a\)
\(3a = g\,\,{\rm{ or, }}a = \frac{g}{3}\)
\( = \frac{{10}}{3} = 3.33\;m/{s^2}\)