JEE MAIN - Physics (2020 - 2nd September Morning Slot - No. 13)
A bead of mass m stays at point P(a, b) on a
wire bent in the shape of a parabola y = 4Cx2
and rotating with angular speed $$\omega $$ (see figure).
The value of $$\omega $$ is (neglect friction) :
_2nd_September_Morning_Slot_en_13_1.png)
$$2\sqrt {2gC} $$
$$2\sqrt {gC} $$
$$\sqrt {{{2gC} \over {ab}}} $$
$$\sqrt {{{2g} \over C}} $$
Explanation
_2nd_September_Morning_Slot_en_13_3.png)
y = 4Cx2
$$ \Rightarrow $$ $$\frac{dy}{dx} $$ = tan $$\theta $$ = 8Cx
At P, tan θ = 8Ca
For steady circular motion
mg sinθ = mω2acosθ
$$ \Rightarrow $$ tan $$\theta $$ = $$\frac{\omega^{2} a}{g} $$
$$ \Rightarrow $$ 8Ca $$ \times $$ g = ω2$$ \times $$a
$$ \Rightarrow $$ $$\omega $$ = $$\sqrt{8gC} $$
$$ \Rightarrow $$ $$\omega $$ = $$2\sqrt {2gC} $$
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