A block of mass 5 kg is being raised vertically upward by the help of a string attached to it. It rises with an acceleration of $2m/s^2$. The block rises by 2.5 m .the work done by tension and work done against gravity are respectively

$(a)\;147.5\;J,-122.5\;J \quad (b)\;122.5\;J,-147.5\;J \quad (c)\;95.5\;J,20.5\;J \quad (d)\;25\;J,-25\;J$

From the free body diagram, $T-mg=5a$
$\Rightarrow T=5(9.8+2) = 59 N$
The force T and the displacement are in the same direction.
Therefore, the Work done by tension $= Ts \cos 0^\circ = 59 \times 2.5 \times 1 = 147.5J$ (here s = 2.5 m, the distance moved by the block)
The gravitational force $mg$ and the displacement are in the opposite direction.
Work done against gravity $=-mgs =5 \times 9.8 \times 2.5 = -122.5J$
edited Aug 25, 2014