They are small elastic balls placed at rest on a smooth horizontal surface which are circulated at the extremes with radius 2m. The masses of balls are M,M2,M22....M2n−1 . Find the least velocity which should be provided to the first ball of mass M such that 5th ball completes a vertical circle (nearly) [in ms−1] .

V2=2m1u1m1+m2 V2=2M(M+M2)u=43u V3=2M2(M2+M4)×43u=(43)2uBetween M4 and M8V4=(43)3uSimilarly V5=(43)4uGiven, V5=5gR=5×2×10=10⇒10=(43)4u⇒u=3.16 m/s

AI Mentor

Check Your IQ

Free Expert Demo

Try Test

Courses

Dropper NEET Course Dropper JEE Course Class - 12 NEET Course Class - 12 JEE Course Class - 11 NEET Course Class - 11 JEE Course Class - 10 Foundation NEET Course Class - 10 Foundation JEE Course Class - 10 CBSE Course Class - 9 Foundation NEET Course Class - 9 Foundation JEE Course Class -9 CBSE Course Class - 8 CBSE Course Class - 7 CBSE Course Class - 6 CBSE Course

Offline Centres

They are small elastic balls placed at rest on a smooth horizontal surface which are circulated at the extremes with radius 2m. The masses of balls are $M, \frac{M}{2}, \frac{M}{2^{2}} .... \frac{M}{2^{n - 1}}$ . Find the least velocity which should be provided to the first ball of mass M such that 5^th ball completes a vertical circle (nearly) $[i n m s^{- 1}]$ .

see full answer

Your Exam Success, Personally Taken Care Of

1:1 expert mentors customize learning to your strength and weaknesses – so you score higher in school , IIT JEE and NEET entrance exams.

An Intiative by Sri Chaitanya

answer is 3.16.

(Unlock A.I Detailed Solution for FREE)

Best Courses for You

JEE

NEET

Foundation JEE

Foundation NEET

CBSE

Detailed Solution

$V_{2} = \frac{2 m_{1} u_{1}}{m_{1} + m_{2}} V_{2} = \frac{2 M}{(M + \frac{M}{2})} u = \frac{4}{3} u$

$V_{3} = \frac{2 \frac{M}{2}}{(\frac{M}{2} + \frac{M}{4})} \times \frac{4}{3} u = {(\frac{4}{3})}^{2} u$

Between $\frac{M}{4} a n d \frac{M}{8}$

$V_{4} = {(\frac{4}{3})}^{3} u$

Similarly $V_{5} = {(\frac{4}{3})}^{4} u$

Given, $V_{5} = \sqrt{5 g R} = \sqrt{5 \times 2 \times 10} = 10$

$\Rightarrow 10 = {(\frac{4}{3})}^{4} u \Rightarrow u = 3.16 m / s$

Watch 3-min video & get full concept clarity

courses

No courses found

Result Producing online coaching for JEE/NEET of south India

Largest All India Test Series for JEE/NEET

Best Online Course for IIT JEE

Best Online Course for NEET

Best Online Course for CBSE

Ready to Test Your Skills?

Check your Performance Today with our Free Mock Test used by Toppers!

Take Free Test

Get Expert Academic Guidance – Connect with a Counselor Today!