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1. Electric Charges and Fields
normal
હિલીયમ ભરેલા બલૂન ઉપર રહેલ સમાન વિદ્યુતભાર કેટલો હોવો જોઇએ?
A
${\left[ {\frac{{mg{r^2}}}{{2k}}\tan \theta } \right]^{1/2}}$
B
${\left[ {\frac{{2k}}{{mg{r^2}}}\tan \theta } \right]^{1/2}}$
C
${\left[ {\frac{{mgr}}{{2k}}\cot \theta } \right]^{1/2}}$
D
${\left[ {\frac{{2k}}{{mgr}}\tan \theta } \right]^{1/2}}$
Solution
$2R = mg$ …. (i)
${F_e} = T\sin \theta $…. (ii)
$R = T\cos \theta $…. (iii)
$2T\cos \theta = mg$ …. (iv)
$\frac{1}{2}\tan \theta = \frac{{{F_e}}}{{mg}}$ ==> $\frac{1}{2}\tan \theta = \frac{{k\frac{{{Q^2}}}{{{r^2}}}}}{{mg}}$$ \Rightarrow $$\theta = {\left( {\frac{{mg{r^2}}}{{2k}}\tan \theta } \right)^{1/2}}$
Standard 12
Physics
