A block of mass 2 kg is being brought down by a string. If the block acquires a speed `1(m)//(s)` in dropping down 25 cm, find the work done by the string in the process.

Explanation

Given, Displacement moved by block `s=25 cm=(1)/(2)m`
initial velocity of block , u=0
Final velocity of block,`v=1ms^(-1)`

From the equation of motion for block,
`v^(2)=u^(2)+2as implies(1)^(2)=0+2axx(1)/(4) implies a=2ms^(-2)`
`:.` Acceleration of the block `a =2ms^(-2)`

For the motion of 2 kg block in downward direction, applying Newton's law we get
`mg-T = ma`
`20-T=2a=2xx2`
`implies T=16N`
`:.` Work done by the string
`W=-Ts=-16xx(1)/(4)=-4 J`
Negative sign indicates the opposite direction of tension and displacement of the block.