Answer
Tension in cord $=89$ $N$
Work Step by Step
Let $m$ be the mass of the lamp and $T$ be the Tension in the cord.
Let the upward direction be $positive$ (sign convention)
Net force is given by:
$F_{net}=ma$
Writing the force equation using proper sign convention gives:
$F_{net}=T-mg$
$ma=T-mg$
Substituting the known values and solving gives:
$2.4m=89-9.8m$
$9.8m+2.4m=89$
$12.2m=89$
$m=\frac{89}{12.2} = 7.29$ $kg$
$m\approx 7.3$ $kg$
Now, it is said that acceleration upwards is $2.4$ $m/s^{2}$.
Writing the force equation using proper sign convention gives:
$F_{net}=T-mg$
$ma=T-mg$
Substituting the known values (now keeping unknown $T$) and solving gives:
$7.3kg \times 2.4m/s^{2}=T- 7.3kg \times 9.8m/s^{2}$
$71.5+17.5=T$
$T=89N$
Actually, both, deceleration of $2.4$ $m/s^{2}$ downwards and acceleration of $2.4$ $m/s^{2}$ upwards are the same thing. So, We get the same Tension in cord in both cases.
