Question

A ball is dropped from a height of 20 m above the surface of water in a lake. The refractive index of water is 4.3. A fish inside the lake, in the line of fall of the ball, is looking at the ball. At an instant, when the ball is 12.8 m above the water surface, the fish sees the speed of the ball as `[Take _(g)=10m/s^(2).]`
A. `9m//s`
B. `12m//s`
C. `16m//s`
D. `21.33m//s`

Answer 1

Correct Answer - C
Speed of the ball`v=sqrt(2gh)`
`v=sqrt(2xx10xx(20-12.8))`
`v=sqrt(2xx10xx7.2)`
`v=12m//s`
For rafraction
`(mu_(2))/(v)-(mu_(1))/(u)=(mu_(2)-mu_(1))/(R)`
For plane surface`R=oo`
`(mu_(w))/(v)-(1)/(u)=0`
` v=,u_(w)xxu`
differnciate the equation with respect to time
`(dv)/(dt)=mu_(w)(du)/(dt)`
`(dv)/(dt)=(4)/(3)xx12`
`(dv)/(dt)=18m//s`