A small body of mass m can slide without friction along

A small body of mass m can slide without friction along a trough bent which is in the form of a semi-circular arc of radius R. At what height h will the body be at rest with respect to the trough, if the trough rotates with uniform angular velocity $ω$ about a vertical axis:

$R - \frac{g}{ω^{2}}$

$R + \frac{2 g}{ω^{2}}$

$R - \frac{2 g}{ω^{2}}$

$R$

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Right Answer is: A

SOLUTION

$∵ N c o s θ = m g$ and $N s i n θ = m ω^{2} r \dots (i)$

$\Rightarrow t a n θ = \frac{ω^{2} r}{g}$

$\Rightarrow \frac{r}{R - h} = \frac{ω^{2} r}{g}$

$\Rightarrow h = R - \frac{g}{ω^{2}}$

A small body of mass m can slide without friction along

Right Answer is: A

SOLUTION

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