AP EAMCET Engineering 22 Apr 2019 Shift 1 Paper

The initial velocity of rain drop will be zero, so u = 0.
The expression of the final velocity of rain drop is,
v=

2gr2(ρ−σ)

9η

By work energy theorem,
W=

1

2

mv2−

1

2

mu2
W=

1

2

mv2−

1

2

m(0)2
W=

1

2

( ρV)v2
W=

1

2

ρ(

4

3

πr3)v2
Substitute the value of v in the above expression.
W=

1

2

ρ(

4

3

πr3)[

2gr2( ρ−σ)2

9η

]2
W∝r7