A stone is projected at angle ' $\theta$ ' with velocity ' $u$ '. If it executes nearly a circular motion at…

A stone is projected at angle ' $\theta$ ' with velocity ' $u$ '. If it executes nearly a circular motion at its maximum point for short time, the radius of the circular path will be ( $\mathrm{g}=$ acceleration due to gravity)
  1. $\frac{\mathrm{u}^2}{\mathrm{~g}}$
  2. $\frac{\mathrm{u}^2 \cos ^2 \theta}{\mathrm{g}}$
  3. $\frac{\mathrm{u}^2 \sin ^2 \theta}{\mathrm{g}}$
  4. $\frac{\mathrm{u}^2 \cos ^2 \theta}{2 \mathrm{~g}}$

Solution

Horizontal velocity at highest point: $\mathrm{v}_{\mathrm{x}}=\mathrm{u}_{\mathrm{x}}=\mathrm{u} \cos \theta$ $\mathrm{a}=\frac{\mathrm{v}_{\mathrm{x}}{ }^2}{\mathrm{R}}$ $a=g$ $\therefore \quad \mathrm{R}=\frac{\mathrm{v}_{\mathrm{x}}{ }^2}{\mathrm{~g}}=\frac{(\mathrm{u} \cos \theta)^2}{\mathrm{~g}}=\frac{\mathrm{u}^2 \cos ^2 \theta}{\mathrm{g}}$

Asked in: MHT CET 2023 (13 May Shift 2)

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