Consider-a-disc-rotating-in-the-horizontal-plane-with-a-constant-angular-speed-about-its-centre-O-The-disc-has-a-shaded-region-on-one-side-of-the-diameter-and-an-unshaded-region-on-the-other-side-a

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Question Number 20745 by Tinkutara last updated on 02/Sep/17

$$\mathrm{Consider}\mathrm{a}\mathrm{disc}\mathrm{rotating}\mathrm{in}\mathrm{the}\mathrm{horizontal}$$$$\mathrm{plane}\mathrm{with}\mathrm{a}\mathrm{constant}\mathrm{angular}\mathrm{speed}\omega$$$$\mathrm{about}\mathrm{its}\mathrm{centre}O.\mathrm{The}\mathrm{disc}\mathrm{has}\mathrm{a}$$$$\mathrm{shaded}\mathrm{region}\mathrm{on}\mathrm{one}\mathrm{side}\mathrm{of}\mathrm{the}\mathrm{diameter}$$$$\mathrm{and}\mathrm{an}\mathrm{unshaded}\mathrm{region}\mathrm{on}\mathrm{the}\mathrm{other}$$$$\mathrm{side}\mathrm{as}\mathrm{shown}\mathrm{in}\mathrm{the}\mathrm{Figure}.\mathrm{When}\mathrm{the}$$$$\mathrm{disc}\mathrm{is}\mathrm{in}\mathrm{the}\mathrm{orientation}\mathrm{as}\mathrm{shown},\mathrm{two}$$$$\mathrm{pebbles}P\mathrm{and}Q\mathrm{are}\mathrm{simultaneously}$$$$\mathrm{projected}\mathrm{at}\mathrm{an}\mathrm{angle}\mathrm{towards}R.\mathrm{The}$$$$\mathrm{velocity}\mathrm{of}\mathrm{projection}\mathrm{is}\mathrm{in}\mathrm{the}y-z$$$$\mathrm{plane}\mathrm{and}\mathrm{is}\mathrm{same}\mathrm{for}\mathrm{both}\mathrm{pebbles}\mathrm{with}$$$$\mathrm{respect}\mathrm{to}\mathrm{the}\mathrm{disc}.\mathrm{Assume}\mathrm{that}\left(i\right)\mathrm{they}$$$$\mathrm{land}\mathrm{back}\mathrm{on}\mathrm{the}\mathrm{disc}\mathrm{before}\mathrm{the}\mathrm{disc}\mathrm{has}$$$$\mathrm{completed}\frac{1}{8}\mathrm{rotation},\left(ii\right)\mathrm{their}\mathrm{range}$$$$\mathrm{is}\mathrm{less}\mathrm{than}\mathrm{half}\mathrm{the}\mathrm{disc}\mathrm{radius},\mathrm{and}$$$$\left(iii\right)\omega \mathrm{remains}\mathrm{constant}\mathrm{throughout}.$$$$\mathrm{Then}$$$$\left(a\right)P\mathrm{lands}\mathrm{in}\mathrm{the}\mathrm{shaded}\mathrm{region}\mathrm{and}Q$$$$\mathrm{in}\mathrm{the}\mathrm{unshaded}\mathrm{region}$$$$\left(b\right)P\mathrm{lands}\mathrm{in}\mathrm{the}\mathrm{unshaded}\mathrm{region}\mathrm{and}$$$$Q\mathrm{in}\mathrm{the}\mathrm{shaded}\mathrm{region}$$$$\left(c\right)\mathrm{Both}P\mathrm{and}Q\mathrm{land}\mathrm{in}\mathrm{the}\mathrm{unshaded}$$$$\mathrm{region}$$$$\left(d\right)\mathrm{Both}P\mathrm{and}Q\mathrm{land}\mathrm{in}\mathrm{the}\mathrm{shaded}$$$$\mathrm{region}$$

Commented by Tinkutara last updated on 02/Sep/17

Commented by NECx last updated on 02/Sep/17

$$howdidyoudrawthis?$$

Commented by Tinkutara last updated on 02/Sep/17

$$\mathrm{I}{\mathrm{didn}}^{\prime }\mathrm{t}\mathrm{drew}\mathrm{this};\mathrm{I}\mathrm{took}\mathrm{screenshot}\mathrm{of}$$$$\mathrm{this}\mathrm{figure}\mathrm{from}\mathrm{a}\mathrm{typed}\mathrm{question}\mathrm{paper}$$$$\mathrm{PDF}.$$

Answered by ajfour last updated on 02/Sep/17

$$bothlandontheunshadedpart.$$$$pointsontheradiusaheadofP$$$$hadlesservelocitiesalongxthan$$$$Phad.$$$$\mathrm{\&}pointsontheradiusaheadof$$$$Qhadgreatervelocitiesalongx$$$$thanQhad.$$

Commented by Tinkutara last updated on 02/Sep/17

$$\mathrm{Thank}\mathrm{you}\mathrm{very}\mathrm{much}\mathrm{Sir}!$$

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