Dear Student, Please find below the solution to the asked query: Given that the angular velocity of the table is, ωtab=π6 rads Now, the angular velocity of the person B with respect to the table is, ω2=v2r-ωtab=v23-π6So,If ω1=5π6 rads and ω2=π3-π6⇒ω2=π6Therefore, the time taken by B to catch A is,t=θω1-ω2=π65π6-π6=14 sIf ω1=4π6 rads and ω2=π3-π6⇒ω2=π6Therefore, the time taken by B to catch A is,t=θω1-ω2=π64π6-π6=13 sIf ω1=4π3 rads and ω2=2π3-π6⇒ω2=π3Therefore, the time taken by B to catch A is,t=θω1-ω2=π64π3-π3=12=0 5 sIf ω1=π6 rads and ω2=2π3-π6⇒ω2=π3Therefore, the anglar velociy of B is more than the angular velocity of A So, A will not reach B within a time 0 2 s Hope this information will clear your doubts about the topic If you have any more doubts just ask here on the forum and our experts will try to help you out as soon as possible Regards

question no. 11

Dear Student,

Please find below the solution to the asked query:

Given that the angular velocity of the table is,

$ω_{t a b} = \frac{π}{6} \frac{r a d}{s}$ .

Now, the angular velocity of the person B with respect to the table is,

$ω_{2} = \frac{v_{2}}{r} - ω_{t a b} = \frac{v_{2}}{3} - \frac{π}{6} S o, I f ω_{1} = \frac{5 π}{6} \frac{r a d}{s} a n d ω_{2} = \frac{π}{3} - \frac{π}{6} \Rightarrow ω_{2} = \frac{π}{6} T h e r e f o r e, t h e t i m e t a k e n b y B t o c a t c h A i s, t = \frac{θ}{ω_{1} - ω_{2}} = \frac{\frac{π}{6}}{\frac{5 π}{6} - \frac{π}{6}} = \frac{1}{4} s I f ω_{1} = \frac{4 π}{6} \frac{r a d}{s} a n d ω_{2} = \frac{π}{3} - \frac{π}{6} \Rightarrow ω_{2} = \frac{π}{6} T h e r e f o r e, t h e t i m e t a k e n b y B t o c a t c h A i s, t = \frac{θ}{ω_{1} - ω_{2}} = \frac{\frac{π}{6}}{\frac{4 π}{6} - \frac{π}{6}} = \frac{1}{3} s I f ω_{1} = \frac{4 π}{3} \frac{r a d}{s} a n d ω_{2} = \frac{2 π}{3} - \frac{π}{6} \Rightarrow ω_{2} = \frac{π}{3} T h e r e f o r e, t h e t i m e t a k e n b y B t o c a t c h A i s, t = \frac{θ}{ω_{1} - ω_{2}} = \frac{\frac{π}{6}}{\frac{4 π}{3} - \frac{π}{3}} = \frac{1}{2} = 0.5 s I f ω_{1} = \frac{π}{6} \frac{r a d}{s} a n d ω_{2} = \frac{2 π}{3} - \frac{π}{6} \Rightarrow ω_{2} = \frac{π}{3} T h e r e f o r e, t h e a n g l a r v e l o c i y o f B i s m o r e t h a n t h e a n g u l a r v e l o c i t y o f A .$

So, A will not reach B within a time 0.2 s.

Hope this information will clear your doubts about the topic.

If you have any more doubts just ask here on the forum and our experts will try to help you out as soon as possible.

Regards

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