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in-a-cup-filled-with-a-liquid-of-density-a-bubble-rests-in-the-liquid-in-h-deepness-radius-initial-of-the-bubble-r-i-initial-density-of-the-bubble-i-mass-amp-temparature-is-constant-a-small

Question Number 227011 by fantastic2 last updated on 25/Dec/25 $${in}\:{a}\:{cup}\:{filled}\:{with}\:{a}\:{liquid}\:{of}\:{density}\:\rho,{a} \\ $$$${bubble}\:{rests}\:{in}\:{the}\:{liquid}\:{in}\:{h}\:{deepness}. \\ $$$${radius}\:{initial}\:{of}\:{the}\:{bubble}={r}_{{i}} \\ $$$$\:{initial}\:{density}\:{of}\:{the}\:{bubble}=\sigma_{{i}} \\ $$$$\left(\:{mass\&temparature}\:{is}\:{constant}\right) \\ $$$${a}\:{small}\:{jerk}\:{is}\:{given}\:{to}\:{the}\:{cup}\:{and}\:{the} \\ $$$${bubble}\:{starts}\:{to}\:{go}\:{upwards}. \\ $$$${find}: \\…

two-small-balls-are-hung-from-a-point-same-mass-same-charge-and-rope-length-are-same-the-two-strings-make-an-angle-30-0-when-immersed-in-a-liquid-of-0-8g-cc-the-angle-remains-same-ball-1-6g

Question Number 226907 by fantastic2 last updated on 18/Dec/25 $${two}\:{small}\:{balls}\:{are}\:{hung}\:{from}\:{a}\:{point} \\ $$$$\left({same}\:{mass},\:{same}\:{charge}\:{and}\:{rope}\:{length}\:{are}\:{same}\right) \\ $$$${the}\:{two}\:{strings}\:{make}\:{an}\:{angle}\:\mathrm{30}^{\mathrm{0}} \\ $$$${when}\:{immersed}\:{in}\:{a}\:{liquid}\:{of}\:\rho=\mathrm{0}.\mathrm{8}{g}/{cc} \\ $$$${the}\:{angle}\:{remains}\:{same}.\rho_{{ball}} =\mathrm{1}.\mathrm{6}{g}/{cc} \\ $$$${what}\:{is}\:{the}\:{value}\:{of}\:\kappa\left({dielectric}\:{const}.\right){of} \\ $$$${the}\:{liquid} \\ $$…

Question-226855

Question Number 226855 by Kassista last updated on 17/Dec/25 Answered by mehdee7396 last updated on 17/Dec/25 $${x}^{\mathrm{2}} +\mathrm{4}{x}^{\mathrm{2}} −\mathrm{4}{x}+\mathrm{4}=\mathrm{4}\Rightarrow{x}=\mathrm{0},\frac{\mathrm{8}}{\mathrm{5}} \\ $$$$\Rightarrow{P}\left(\mathrm{0},,\mathrm{2}\right)\:\&\:\:{Q}\left(\frac{\mathrm{8}}{\mathrm{5}},−\frac{\mathrm{6}}{\mathrm{5}}\right)\Rightarrow{m}_{{PQ}} =−\frac{\mathrm{3}}{\mathrm{4}} \\ $$$$\Rightarrow{tan}\alpha=\frac{\mathrm{3}}{\mathrm{4}}\backsimeq\mathrm{36}^{\mathrm{0}} \Rightarrow\angle{POQ}\backsimeq\mathrm{126}^{\mathrm{0}}…

Question-226785

Question Number 226785 by fantastic2 last updated on 14/Dec/25 Commented by fantastic2 last updated on 15/Dec/25 $${there}\:{are}\:{three}\:{small}\:{balls}\:{of}\:{mass}\:{m}_{\mathrm{1},} {m}_{\mathrm{2}} \:{and}\:{m}_{\mathrm{3}} \\ $$$${all}\:{are}\:{hanging}\:{from}\:{a}\:{point}\:{O}\:{by}\:{a}\:{string} \\ $$$${length}\:{l}\:. \\ $$$${what}\:{charge}\:{should}\:{be}\:{given}\:{to}\:{them}\:{so}…

Question-226755

Question Number 226755 by Hanuda354 last updated on 13/Dec/25 Answered by TonyCWX last updated on 13/Dec/25 $${A}_{{Green}} =\frac{\mathrm{1}}{\mathrm{2}}\left(\mathrm{8}^{\mathrm{2}} \right)\left(\frac{\pi}{\mathrm{3}}\right)+\frac{\mathrm{1}}{\mathrm{2}}\left(\mathrm{8}^{\mathrm{2}} \right)\left(\frac{\pi}{\mathrm{3}}−\frac{\sqrt{\mathrm{3}}}{\mathrm{2}}\right)−\frac{\mathrm{1}}{\mathrm{2}}\pi\left(\mathrm{4}^{\mathrm{2}} \right)=\frac{\mathrm{40}}{\mathrm{3}}\pi−\mathrm{16}\sqrt{\mathrm{3}} \\ $$$${A}_{{Blue}\:} =\:\left(\frac{\mathrm{12}−\mathrm{3}\sqrt{\mathrm{3}}−\mathrm{2}\pi}{\mathrm{12}}\right)\left(\mathrm{8}^{\mathrm{2}} \right)=\mathrm{64}−\mathrm{16}\sqrt{\mathrm{3}}−\frac{\mathrm{32}}{\mathrm{3}}\pi…