Q - 8

Asked by majethiyarishat9566.12sdatl | 21st Jun, 2020, 01:49: PM

Expert Answer:

Fig shows a plastic ball of mass m suspended by a light string in a uniform field of intensity E. 
I t apostrophe s space g i v e n space t h a t space t h e space p a r t i c l e space c o m e s space t o space e q u i l i b r i u m space a t space a n space a n g l e space theta space w. r. t space h o r i z o n t a l
W h e n space e l e c t r i c space f i e l d space a c t s space a l o n g space a space d i r e c t i o n space w h i c h space m a k e s space a n space a n g l e space theta space w i t h space h o r i z o n t a l space t h e n space t h e space f o r c e s space a c t i n g space o n space t h e space b a l l space a r e space
F subscript v e r t i c a l end subscript space equals space m g space minus space q E subscript y space
F subscript h o r i z o n t a l space end subscript equals space q E subscript x space
tan theta space equals space F subscript h o r i z o n t a l space end subscript over F subscript v e r t i c a l end subscript space equals space fraction numerator space q E subscript x over denominator m g space minus space q E subscript y end fraction
rightwards double arrow space q E subscript x space equals space m g space tan theta space minus space q E subscript y tan theta
therefore q space equals space fraction numerator m g tan theta over denominator E subscript x plus E subscript y tan theta space end fraction
S o l v i n g space w e space g e t comma space
q space equals space fraction numerator m g over denominator co t space theta left parenthesis E subscript x space plus space E subscript y left parenthesis begin display style fraction numerator 1 over denominator c o t theta end fraction end style right parenthesis end fraction space equals space fraction numerator m g over denominator E subscript x space c o t theta space plus space E subscript y end fraction
T e n s i o n space i n space t h e space s t r i n g space i s space g i v e n space a s comma space
T space equals space square root of open parentheses F subscript h o r i z o n t a l space end subscript close parentheses squared plus open parentheses F subscript v e r t i c a l end subscript close parentheses squared end root space equals space square root of space open parentheses q E subscript x close parentheses squared plus open parentheses m g space minus space q E subscript y close parentheses squared space end root space
O n space s o l v i n g space w e space g e t comma space
space T space equals space fraction numerator m g space E subscript x over denominator E subscript x cos plus E subscript y sin theta end fraction

Answered by Shiwani Sawant | 22nd Jun, 2020, 10:00: PM