A table with smooth horizontal surface is turning at an angular speed `omega` about its axis. A groove is made on the surface along a radius and a particle is gently placed inside the groove at a distance a from the centre. Find the speed of the speed of the particle as its distance from teh centre becomes L.

A table with smooth horizontal surface is turning at an angular speed

1.	A table with smooth horizontal surface is turning at an angular speed `omega` about its axis. A groove is made on the surface along a radius and a particle is gently placed inside the groove at a distance a from the centre. Find the speed of the speed of the particle as its distance from teh centre becomes L.
Answer» Correct Answer - A::B At distance `x` from centre, Centrifugal force `a=xomega^(2)` ltbr. Or `v(dv)/(dx)=xomega^(2)` or `int_(0)^(v)vdv=omega^(2)int_(a)^(L)xdx` or `(v^(2))/(2)=(omega^(2))/(2)(L^(2)-a^(2))` or `v=omegasqrt(L^(2)-a^(2))`

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