Question

=A hemispherical boel of radius R is rotating about its own ( vertical ) with an angular velocity 'w' . a particle of mass 10^-2 on the frictionless inner surface of the bowl is also rotating with same velocity . the particle of height h from the bottom bowl . the condition to be satisfied to te non zero value of h is -----
a) w > (g/R)^1/2
b) w < (g/R)^1/2
c) w > (g/R)^1/2
d) w = (g/R)^1/2

Answer 1

ANSWER....

FOR A PARTICLE REMAINS AT HEIGHT h WE NEED TO UNDERSTAND SOME CONDITION FOR THIS TO BE HAPPEN.

THE CENTRIFUGAL FORCE ACTING ON THE PARTICLE SHOULD BE EQUAL OR MORE THAN THE WEIGHT OF THE BODY SO THAT IT COULD BALANCE THE BODY AND PREVENT IT FROM SLIDING AND GIVE A ZERO h.....[✓]

• CENTRIFUGAL FORCE

WHEN WE ARE IN ACCELERATED FRAME AND ROTATING WITH SOME ANGULAR ACCELERATION THAN A FORCE IS ACTING ON THE BODY RADIALLY OUTWARD KNOWN AS CENTRIFUGAL FORCE.....[✓]

$m {w}^{2} r \geqslant mg \\ \\ {w}^{2} \geqslant \frac{g}{r} \\ \\ w \geqslant { (\frac{g}{r} )}^{ \frac{1}{2} } .....answer \\ \\ where \: w \: is \: the \: angular \: velocity \\ r \: is \: the \: radius \: of \: circle \: track \\ \\ mg \: is \: the \: weight \: of \: the \: body$

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