Question

A particle is revolving in a circle of radius R with initial velocity u . Its start ts retarding with constant retardation v^2/4πR . The number of revolutions it makes in time 8πR/u is.!?

Answer 1

Distance moved by particle along circle before coming to restv2−u2=2as0−v2=−2asv2=2asv2=2ass=v22a=v2×4π×R2×v2=2πRangle moved=distance movedradiusθ=2πRR=2π which is equal to one revolutiontime taken by particle to stopv=u−at0=v−v2t4πRt=4πRvTime left for the particle to move 8πRv−4πRv=4πRvNow the particle stops for a moment and starts rotating in opposite directionDistance moved by particle along circle in time 4πRv starting from rests=ut+12at2=12at2=v24πR×(4πRv)22=2πRθ=2πRR=2π which is equal to one revolution S0 total number of rotation is 2

Answer 2

Answer:

F=MV2/r

F is inversely proportional to r

then v=r*omega

omega=2pie/t

v=2pie*r/t

then

f = 4\ {\pi}^{2} {r}^{2} \div {t}^{2} \times r

then f is inversely proportional to time