The two ends of a rubber string of negligible mass and having unstretched length `24cm` are fixed at the some height as shown. A small object is attached to the string in its midpoint due to which the depression `h` of the object in equilibrium is `5cm`. Then the small object is charged and a vertical electric field `E_(1)` is switched on in the region. The equilibrium depression of the object increases to `9cm`, now the electric field is changed to `E_(2)` and the depression of object in equilibrium increases to `16cm`. What is the ratio of electric field in the second case to that of in the first case ?

Answer

`0017`

Explanation

Initially `2Tcostheta=mg`…..(1)
`here T=k(26-24)`
`T=2k`
So, `2xx2kxx5/13=mg` …..(A)
1st Case Now length of string = 30 cm
`T_(1)=k(30-24)`
`:.2T_(1)cosphi=qE_(1)+mg`
`2xx6kxx9/15=qE_(1)+mg`
`:.36/5k-20/13k=qE_(1)`
`((468-100)k)/65 = qE_(1)`
`:.(368k)/65 = qE_(1)` .....(B)
2nd Case `T_(2)=k(40-24)=16k`
`2xx16kxx16/20=qE_(2)+mg`
`:.qE_(2)=(128k)/5-(20k)/13=((1664-100)k)/65`
`qE_(2)=1564/65 k` ....(C)
:.`E_(2)/E_(1)=1564/368=4.25`