Question Number 24879 by Tinkutara last updated on 28/Nov/17 $$\mathrm{A}\:\mathrm{particle}\:\mathrm{of}\:\mathrm{mass}\:{m}\:\mathrm{is}\:\mathrm{fixed}\:\mathrm{to}\:\mathrm{one}\:\mathrm{end} \\ $$$$\mathrm{of}\:\mathrm{a}\:\mathrm{light}\:\mathrm{rigid}\:\mathrm{rod}\:\mathrm{of}\:\mathrm{length}\:{l}\:\mathrm{and}\:\mathrm{rotated} \\ $$$$\mathrm{in}\:\mathrm{a}\:\mathrm{vertical}\:\mathrm{circular}\:\mathrm{path}\:\mathrm{about}\:\mathrm{its} \\ $$$$\mathrm{other}\:\mathrm{end}.\:\mathrm{The}\:\mathrm{minimum}\:\mathrm{speed}\:\mathrm{of}\:\mathrm{the} \\ $$$$\mathrm{particle}\:\mathrm{at}\:\mathrm{its}\:\mathrm{highest}\:\mathrm{point}\:\mathrm{must}\:\mathrm{be} \\ $$ Commented by ajfour last updated…
Question Number 24877 by Tinkutara last updated on 28/Nov/17 Commented by Tinkutara last updated on 28/Nov/17 Commented by mrW1 last updated on 29/Nov/17 $${mg}−{T}={ma} \\…
Question Number 24873 by Tinkutara last updated on 28/Nov/17 $$\mathrm{A}\:\mathrm{rigid}\:\mathrm{body}\:\mathrm{is}\:\mathrm{made}\:\mathrm{of}\:\mathrm{three}\:\mathrm{identical} \\ $$$$\mathrm{thin}\:\mathrm{rods},\:\mathrm{each}\:\mathrm{of}\:\mathrm{length}\:{L},\:\mathrm{fastened} \\ $$$$\mathrm{together}\:\mathrm{in}\:\mathrm{the}\:\mathrm{form}\:\mathrm{of}\:\mathrm{letter}\:{H}.\:\mathrm{The} \\ $$$$\mathrm{body}\:\mathrm{is}\:\mathrm{free}\:\mathrm{to}\:\mathrm{rotate}\:\mathrm{about}\:\mathrm{a}\:\mathrm{horizontal} \\ $$$$\mathrm{axis}\:\mathrm{that}\:\mathrm{runs}\:\mathrm{along}\:\mathrm{the}\:\mathrm{length}\:\mathrm{of}\:\mathrm{one}\:\mathrm{of} \\ $$$$\mathrm{legs}\:\mathrm{of}\:{H}.\:\mathrm{The}\:\mathrm{body}\:\mathrm{is}\:\mathrm{allowed}\:\mathrm{to}\:\mathrm{fall} \\ $$$$\mathrm{from}\:\mathrm{rest}\:\mathrm{from}\:\mathrm{a}\:\mathrm{position}\:\mathrm{in}\:\mathrm{which}\:\mathrm{plane} \\ $$$$\mathrm{of}\:{H}\:\mathrm{is}\:\mathrm{horizontal}.\:\mathrm{The}\:\mathrm{angular}\:\mathrm{speed} \\…
Question Number 24858 by Tinkutara last updated on 27/Nov/17 $$\mathrm{If}\:\mathrm{three}\:\mathrm{positive}\:\mathrm{numbers}\:{a},\:{b},\:{c}\:\mathrm{are}\:\mathrm{in} \\ $$$$\mathrm{A}.\mathrm{P}.\:\mathrm{and}\:\frac{\mathrm{1}}{{a}^{\mathrm{2}} },\:\frac{\mathrm{1}}{{b}^{\mathrm{2}} },\:\frac{\mathrm{1}}{{c}^{\mathrm{2}} }\:\mathrm{also}\:\mathrm{in}\:\mathrm{A}.\mathrm{P}.,\:\mathrm{then} \\ $$$$\left(\mathrm{1}\right)\:{a}\:=\:{b}\:=\:{c} \\ $$$$\left(\mathrm{2}\right)\:\mathrm{2}{b}\:=\:\mathrm{3}{a}\:+\:{c} \\ $$$$\left(\mathrm{3}\right)\:{b}^{\mathrm{2}} \:=\:\frac{{ac}}{\mathrm{8}} \\ $$$$\left(\mathrm{4}\right)\:\mathrm{2}{c}\:=\:\mathrm{2}{b}\:+\:{a} \\…
Question Number 24814 by Tinkutara last updated on 26/Nov/17 Commented by Tinkutara last updated on 26/Nov/17 Commented by ajfour last updated on 27/Nov/17 $${either}\:{launch},\:{same}\:{amplitude}. \\…
Question Number 24786 by Tinkutara last updated on 26/Nov/17 $$\mathrm{A}\:\mathrm{particle}\:\mathrm{of}\:\mathrm{mass}\:{m}\:\mathrm{is}\:\mathrm{moving}\:\mathrm{in}\:{yz}-\mathrm{plane} \\ $$$$\mathrm{with}\:\mathrm{a}\:\mathrm{uniform}\:\mathrm{velocity}\:{v}\:\mathrm{with}\:\mathrm{its} \\ $$$$\mathrm{trajectory}\:\mathrm{running}\:\mathrm{parallel}\:\mathrm{to}\:+\mathrm{ve}\:{y}- \\ $$$$\mathrm{axis}\:\mathrm{and}\:\mathrm{intersecting}\:{z}-\mathrm{axis}\:\mathrm{at}\:{z}\:=\:{a}. \\ $$$$\mathrm{The}\:\mathrm{change}\:\mathrm{in}\:\mathrm{its}\:\mathrm{angular}\:\mathrm{momentum} \\ $$$$\mathrm{about}\:\mathrm{the}\:\mathrm{origin}\:\mathrm{as}\:\mathrm{it}\:\mathrm{bounces}\:\mathrm{elastically} \\ $$$$\mathrm{from}\:\mathrm{a}\:\mathrm{wall}\:\mathrm{at}\:{y}\:=\:\mathrm{constant}\:\mathrm{is}\:: \\ $$$$\left(\mathrm{1}\right)\:{mva}\overset{\wedge} {{e}}_{{x}}…
Question Number 90316 by M±th+et£s last updated on 22/Apr/20 $$\begin{vmatrix}{{x}}&{\mathrm{7}}\\{\mathrm{9}}&{\mathrm{8}−{x}}\end{vmatrix}=\begin{vmatrix}{\mathrm{7}}&{\mathrm{0}}&{−\mathrm{3}}\\{−\mathrm{5}}&{{x}}&{−\mathrm{6}}\\{−\mathrm{3}}&{−\mathrm{5}}&{{x}−\mathrm{9}}\end{vmatrix} \\ $$$$ \\ $$ Commented by john santu last updated on 23/Apr/20 $$\mathrm{8}{x}−{x}^{\mathrm{2}} −\mathrm{63}\:=\:\mathrm{7}\left({x}^{\mathrm{2}} −\mathrm{9}{x}−\mathrm{30}\right)−…
Question Number 24772 by Tinkutara last updated on 25/Nov/17 $$\mathrm{The}\:\mathrm{ratio}\:\mathrm{of}\:\mathrm{acceleration}\:\mathrm{of}\:\mathrm{points}\:{A}, \\ $$$${B}\:\mathrm{and}\:{C}\:\mathrm{is}\:\left[\mathrm{assume}\:\mathrm{all}\:\mathrm{surfaces}\:\mathrm{are}\right. \\ $$$$\left.\mathrm{smooth},\:\mathrm{pulley}\:\mathrm{and}\:\mathrm{strings}\:\mathrm{are}\:\mathrm{light}\right] \\ $$ Commented by Tinkutara last updated on 25/Nov/17 Commented by…
Question Number 24739 by Tinkutara last updated on 25/Nov/17 $${A}\:{particle}\:{is}\:{suspended}\:{vertically} \\ $$$${from}\:{point}\:{O}\:{by}\:{ideal}\:{string}\:{of}\:{length} \\ $$$${L}.\:{It}\:{is}\:{given}\:{horizontal}\:{velocity}\:'{v}'. \\ $$$${There}\:{is}\:{vertical}\:{line}\:{AB}\:{at}\:{a}\:{distance} \\ $$$$\frac{{L}}{\mathrm{8}}\:{from}\:{P}.\:{At}\:{some}\:{point},\:{it}\:{leaves} \\ $$$${circular}\:{motion}\:{and}\:{follows}\:{projectile} \\ $$$${motion}.\:{At}\:{the}\:{instant}\:{it}\:{crosses}\:{AB}, \\ $$$${its}\:{velocity}\:{is}\:{horizontal}.\:{Find}\:{u} \\…
Question Number 24730 by Tinkutara last updated on 25/Nov/17 $$\mathrm{Consider}\:\mathrm{a}\:\mathrm{uniform}\:\mathrm{square}\:\mathrm{plate}\:\mathrm{of}\:\mathrm{side} \\ $$$${a}\:\mathrm{and}\:\mathrm{mass}\:{m}.\:\mathrm{The}\:\mathrm{moment}\:\mathrm{of}\:\mathrm{inertia} \\ $$$$\mathrm{of}\:\mathrm{this}\:\mathrm{plate}\:\mathrm{about}\:\mathrm{an}\:\mathrm{axis}\:\mathrm{perpendicular} \\ $$$$\mathrm{to}\:\mathrm{its}\:\mathrm{plane}\:\mathrm{and}\:\mathrm{passing}\:\mathrm{through}\:\mathrm{one}\:\mathrm{of} \\ $$$$\mathrm{its}\:\mathrm{corners}\:\mathrm{is} \\ $$ Commented by ajfour last updated…