Question Number 24716 by Tinkutara last updated on 25/Nov/17 $$\mathrm{A}\:\mathrm{2}.\mathrm{2}\:\mathrm{kg}\:\mathrm{block}\:\mathrm{starts}\:\mathrm{from}\:\mathrm{rest}\:\mathrm{on}\:\mathrm{a} \\ $$$$\mathrm{rough}\:\mathrm{inclined}\:\mathrm{plane}\:\mathrm{that}\:\mathrm{makes}\:\mathrm{an} \\ $$$$\mathrm{angle}\:\mathrm{of}\:\mathrm{25}°\:\mathrm{with}\:\mathrm{the}\:\mathrm{horizontal}.\:\mathrm{The} \\ $$$$\mathrm{coefficient}\:\mathrm{of}\:\mathrm{kinetic}\:\mathrm{friction}\:\mathrm{is}\:\mathrm{0}.\mathrm{25}.\:\mathrm{As} \\ $$$$\mathrm{the}\:\mathrm{block}\:\mathrm{goes}\:\mathrm{2}\:\mathrm{m}\:\mathrm{down}\:\mathrm{the}\:\mathrm{plane},\:\mathrm{the} \\ $$$$\mathrm{mechanical}\:\mathrm{energy}\:\mathrm{of}\:\mathrm{the}\:\mathrm{Earth}-\mathrm{block} \\ $$$$\mathrm{system}\:\mathrm{changes}\:\mathrm{by} \\ $$ Answered…
Question Number 24712 by ajfour last updated on 25/Nov/17 Commented by ajfour last updated on 25/Nov/17 $${Originally}\:{a}\:{planet}\:{of}\:{radius}\:\boldsymbol{{R}}, \\ $$$${of}\:{uniform}\:{density},\:{has}\:{a}\:{gravitational} \\ $$$${field}\:{at}\:{its}\:{surface}\:{equal}\:{to}\:\:\boldsymbol{{g}}. \\ $$$${Because}\:{a}\:{sphere}\:{of}\:{crust}\:{of} \\ $$$${radius}\:\boldsymbol{{r}}\:{is}\:{removed}\:{gravitational}…
Question Number 24687 by Tinkutara last updated on 24/Nov/17 $$\mathrm{A}\:\mathrm{particle}\:\mathrm{starts}\:\mathrm{from}\:\mathrm{rest}\:\mathrm{at}\:{t}\:=\:\mathrm{0}\:\mathrm{and} \\ $$$$\mathrm{moves}\:\mathrm{with}\:\mathrm{uniform}\:\mathrm{acceleration}.\:\mathrm{Then} \\ $$$$\left(\mathrm{1}\right)\:\mathrm{In}\:\mathrm{any}\:\mathrm{time}\:\mathrm{interval}\:\mathrm{starting}\:\mathrm{from} \\ $$$${t}\:=\:\mathrm{0}\:\mathrm{the}\:\mathrm{space}-\mathrm{average}\:\mathrm{of}\:\mathrm{the}\:\mathrm{velocity} \\ $$$$\mathrm{is}\:\frac{\mathrm{4}}{\mathrm{3}}\:\mathrm{times}\:\mathrm{of}\:\mathrm{time}\:\mathrm{average}\:\mathrm{velocity} \\ $$$$\left(\mathrm{2}\right)\:\mathrm{If}\:{v}\:=\:{v}_{\mathrm{1}} \:\mathrm{at}\:{t}\:=\:{t}_{\mathrm{1}} \:\mathrm{and}\:{v}\:=\:{v}_{\mathrm{2}} \:\mathrm{at}\:{t}\:=\:{t}_{\mathrm{2}} \\ $$$$\mathrm{then}\:\mathrm{time}\:\mathrm{average}\:\mathrm{velocity}\:\mathrm{between}\:{t}_{\mathrm{1}}…
Question Number 24685 by Tinkutara last updated on 24/Nov/17 $$\mathrm{The}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{the}\:\mathrm{kinetic}\:\mathrm{and}\:\mathrm{potential} \\ $$$$\mathrm{energies}\:\mathrm{of}\:\mathrm{a}\:\mathrm{system}\:\mathrm{of}\:\mathrm{objects}\:\mathrm{is}\:\mathrm{conserved} \\ $$$$\left(\mathrm{1}\right)\:\mathrm{Only}\:\mathrm{when}\:\mathrm{no}\:\mathrm{external}\:\mathrm{force}\:\mathrm{acts}\:\mathrm{on} \\ $$$$\mathrm{the}\:\mathrm{objects} \\ $$$$\left(\mathrm{2}\right)\:\mathrm{Only}\:\mathrm{when}\:\mathrm{the}\:\mathrm{objects}\:\mathrm{move}\:\mathrm{along} \\ $$$$\mathrm{closed}\:\mathrm{paths} \\ $$$$\left(\mathrm{3}\right)\:\mathrm{Only}\:\mathrm{when}\:\mathrm{the}\:\mathrm{work}\:\mathrm{done}\:\mathrm{by}\:\mathrm{the} \\ $$$$\mathrm{resultant}\:\mathrm{external}\:\mathrm{force}\:\mathrm{is}\:\mathrm{zero} \\…
Question Number 24667 by tawa tawa last updated on 24/Nov/17 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 24662 by NECx last updated on 24/Nov/17 $$\boldsymbol{{solve}}\:\mid{x}^{\mathrm{2}} −\mathrm{4}{x}−\mathrm{5}\mid=\mathrm{7} \\ $$$$ \\ $$ Answered by mrW1 last updated on 24/Nov/17 $${x}^{\mathrm{2}} −\mathrm{4}{x}−\mathrm{5}=\pm\mathrm{7} \\…
Question Number 24647 by tawa tawa last updated on 23/Nov/17 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 24644 by Tinkutara last updated on 23/Nov/17 $$\mathrm{The}\:\mathrm{density}\:\mathrm{of}\:\mathrm{a}\:\mathrm{non}-\mathrm{uniform}\:\mathrm{rod}\:\mathrm{of} \\ $$$$\mathrm{length}\:\mathrm{1}\:\mathrm{m}\:\mathrm{is}\:\mathrm{given}\:\mathrm{by}\:\rho\left({x}\right)\:=\:{a}\left(\mathrm{1}\:+\:{bx}^{\mathrm{2}} \right) \\ $$$$\mathrm{where}\:{a}\:\mathrm{and}\:{b}\:\mathrm{are}\:\mathrm{constants}\:\mathrm{and} \\ $$$$\mathrm{0}\:\leqslant\:{x}\:\leqslant\:\mathrm{1}.\:\mathrm{The}\:\mathrm{centre}\:\mathrm{of}\:\mathrm{mass}\:\mathrm{of}\:\mathrm{the}\:\mathrm{rod} \\ $$$$\mathrm{will}\:\mathrm{be}\:\mathrm{at} \\ $$$$\left(\mathrm{1}\right)\:\frac{\mathrm{3}\left(\mathrm{2}\:+\:{b}\right)}{\mathrm{4}\left(\mathrm{3}\:+\:{b}\right)} \\ $$$$\left(\mathrm{2}\right)\:\frac{\mathrm{4}\left(\mathrm{2}\:+\:{b}\right)}{\mathrm{3}\left(\mathrm{3}\:+\:{b}\right)} \\ $$$$\left(\mathrm{3}\right)\:\frac{\mathrm{3}\left(\mathrm{3}\:+\:{b}\right)}{\mathrm{4}\left(\mathrm{2}\:+\:{b}\right)}…
Question Number 24635 by tawa tawa last updated on 23/Nov/17 $$\mathrm{Calculate}\:\mathrm{the}\:\mathrm{electric}\:\mathrm{potential}\:\mathrm{at}\:\mathrm{a}\:\mathrm{point}\:\mathrm{P}\:\mathrm{at}\:\mathrm{a}\:\mathrm{distance}\:\mathrm{of}\:\mathrm{3m}\:\mathrm{of}\:\mathrm{either} \\ $$$$\mathrm{charges}\:\mathrm{of}\:\:+\mathrm{20}\:\mu\mathrm{C}\:\mathrm{and}\:\:−\:\mathrm{15}\mu\mathrm{C}.\:\:\mathrm{which}\:\mathrm{are}\:\mathrm{25cm}\:\mathrm{apart}. \\ $$$$\mathrm{Also}\:\mathrm{calculate}\:\mathrm{potential}\:\mathrm{energy}\:\mathrm{of}\:\mathrm{a}\:\:+\mathrm{3}.\mathrm{5}\mu\mathrm{C}\:\mathrm{placed}\:\mathrm{at}\:\mathrm{point}\:\mathrm{P}. \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 24628 by ajfour last updated on 23/Nov/17 Commented by ajfour last updated on 23/Nov/17 $${m}_{\mathrm{1}} \:{hits}\:{m}_{\mathrm{2}} \:{elastically},\:{then} \\ $$$${m}_{\mathrm{2}} \:{hits}\:{m}_{\mathrm{3}} .\:{So}\:{that}\:\:{m}_{\mathrm{3}} \:{acquires} \\…