13 no.

Asked by Harshhacker2580 | 28th Apr, 2020, 11:20: AM

Expert Answer:

if v is the speed of bead at A , then its kinetic energy = (1/2) m v2
Forces acting on the bead = -mg - k ( x - R )
first term on RHS is due to weight and second term is due to spring force when spring is elongated to a distance x.
R is adius of hoop and also equals to natural length of spring
Hence workdone W on the bead  is given by
begin mathsize 14px style W space equals space integral subscript 2 R end subscript superscript R left square bracket negative m g space minus space k space left parenthesis x space minus space R right parenthesis space right square bracket space d x end style = mgR +(1/2) k R2
By work-energy theorem  , (1/2) m v2 = ( m g R ) + (1/2) k R2
Hence velocity of bead at A ,  v = [ ( 2 g R ) + (k/m) R2 ]1/2

Answered by Thiyagarajan K | 28th Apr, 2020, 04:07: PM

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