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A-compound-pendulum-oscillates-though-a-small-angle-about-its-equilibrium-position-such-that-10a-d-dt-2-4g-cos-a-gt-0-its-period-is-A-2pi-5a-4g-B-2pi-5-a-g-

Question Number 84231 by Rio Michael last updated on 10/Mar/20 $$\mathrm{A}\:\mathrm{compound}\:\mathrm{pendulum}\:\mathrm{oscillates}\:\mathrm{though}\:\mathrm{a} \\ $$$$\mathrm{small}\:\mathrm{angle}\:\theta\:\mathrm{about}\:\mathrm{its}\:\mathrm{equilibrium}\:\mathrm{position} \\ $$$$\mathrm{such}\:\mathrm{that} \\ $$$$\:\:\:\mathrm{10}{a}\left(\frac{{d}\theta}{{dt}}\right)^{\mathrm{2}} \:=\:\mathrm{4}{g}\:\mathrm{cos}\:\theta\:,\:{a}\:>\mathrm{0}\:.\:\mathrm{its}\:\mathrm{period}\:\mathrm{is}\: \\ $$$$\left[\mathrm{A}\right]\:\mathrm{2}\pi\sqrt{\frac{\mathrm{5}{a}}{\mathrm{4}{g}}\:\:}\:\:\:\left[\mathrm{B}\right]\:\frac{\mathrm{2}\pi}{\mathrm{5}}\sqrt{\frac{{a}}{{g}}}\:\:\left[\mathrm{C}\right]\:\mathrm{2}\pi\sqrt{\frac{\mathrm{2}{g}}{\mathrm{5}{a}}\:}\:\:\left[\mathrm{D}\right]\:\mathrm{2}\pi\sqrt{\frac{\mathrm{5}{a}}{{g}}}\: \\ $$ Answered by TANMAY…

find-the-distance-between-the-planes-2x-y-z-24-and-2x-y-z-36-

Question Number 84218 by Rio Michael last updated on 10/Mar/20 $$\mathrm{find}\:\mathrm{the}\:\mathrm{distance}\:\mathrm{between}\:\mathrm{the}\:\mathrm{planes} \\ $$$$\:\mathrm{2}\boldsymbol{{x}}−\boldsymbol{{y}}−\boldsymbol{{z}}\:=\:\mathrm{24}\:\mathrm{and}\:\mathrm{2}\boldsymbol{{x}}−\boldsymbol{{y}}−\boldsymbol{{z}}\:=\:\mathrm{36} \\ $$ Commented by M±th+et£s last updated on 10/Mar/20 $$\mathrm{2}{x}−{y}−{z}=\mathrm{24}\Rightarrow\Rightarrow\mathrm{2}{x}−{y}−{z}−\mathrm{24}=\mathrm{0} \\ $$$$\mathrm{2}{x}−{y}−{z}=\mathrm{36}\Rightarrow\Rightarrow\mathrm{2}{x}−{y}−{z}−\mathrm{36}=\mathrm{0}…

find-the-maximum-value-of-2-3cosh2x-2-

Question Number 84220 by Rio Michael last updated on 10/Mar/20 $$\mathrm{find}\:\mathrm{the}\:\mathrm{maximum}\:\mathrm{value}\:\mathrm{of}\:\frac{\mathrm{2}}{\mathrm{3cosh2}{x}\:+\mathrm{2}} \\ $$ Commented by mr W last updated on 10/Mar/20 $$\mathrm{cosh}\:\mathrm{2}{x}\:\geqslant\mathrm{1} \\ $$$$\mathrm{3}\:\mathrm{cosh}\:\mathrm{2}{x}+\mathrm{2}\:\geqslant\mathrm{3}×\mathrm{1}+\mathrm{2}=\mathrm{5} \\…

An-elastic-material-has-a-length-of-36cm-when-a-load-of-40N-is-hung-on-it-and-a-length-of-45cm-when-a-load-of-60N-is-hung-on-it-what-is-the-Original-length-of-the-string-

Question Number 18666 by tawa tawa last updated on 26/Jul/17 $$\mathrm{An}\:\mathrm{elastic}\:\mathrm{material}\:\mathrm{has}\:\mathrm{a}\:\mathrm{length}\:\mathrm{of}\:\:\mathrm{36cm}\:\mathrm{when}\:\mathrm{a}\:\mathrm{load}\:\mathrm{of}\:\mathrm{40N}\:\mathrm{is}\:\mathrm{hung}\:\mathrm{on}\:\mathrm{it}\:\mathrm{and} \\ $$$$\mathrm{a}\:\mathrm{length}\:\mathrm{of}\:\mathrm{45cm}\:\mathrm{when}\:\mathrm{a}\:\mathrm{load}\:\mathrm{of}\:\mathrm{60N}\:\mathrm{is}\:\mathrm{hung}\:\mathrm{on}\:\mathrm{it}.\:\mathrm{what}\:\mathrm{is}\:\mathrm{the}\:\mathrm{Original}\: \\ $$$$\mathrm{length}\:\mathrm{of}\:\mathrm{the}\:\mathrm{string}\:? \\ $$ Answered by mrW1 last updated on 27/Jul/17 $$\mathrm{36}−\frac{\mathrm{45}−\mathrm{36}}{\mathrm{60}−\mathrm{40}}×\mathrm{40}=\mathrm{18}\:\mathrm{cm}…

Argon-diffuses-through-a-hole-under-prescribed-condition-of-temperature-and-pressure-at-the-rate-of-3cm-3-per-velocity-At-what-velocity-will-helium-diffuse-through-the-same-hole-under-the-same-con

Question Number 18624 by tawa tawa last updated on 25/Jul/17 $$\mathrm{Argon}\:\mathrm{diffuses}\:\mathrm{through}\:\mathrm{a}\:\mathrm{hole}\:\mathrm{under}\:\mathrm{prescribed}\:\mathrm{condition}\:\mathrm{of}\:\mathrm{temperature} \\ $$$$\mathrm{and}\:\mathrm{pressure}\:\mathrm{at}\:\mathrm{the}\:\mathrm{rate}\:\mathrm{of}\:\:\mathrm{3cm}^{\mathrm{3}} \:\mathrm{per}\:\mathrm{velocity}.\:\mathrm{At}\:\mathrm{what}\:\mathrm{velocity}\:\mathrm{will}\:\mathrm{helium}\: \\ $$$$\mathrm{diffuse}\:\mathrm{through}\:\mathrm{the}\:\mathrm{same}\:\mathrm{hole}\:\mathrm{under}\:\mathrm{the}\:\mathrm{same}\:\mathrm{condition}\: \\ $$$$\left(\mathrm{Ar}\:=\:\mathrm{29}.\mathrm{94}\:\mathrm{g},\:\:\mathrm{He}\:=\:\mathrm{4g}\right). \\ $$ Answered by Tinkutara last updated…