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QJEEM20Phc1ec: JEE Main 2020 Physics - Class 11 JEEM20Phc1ec Solution: One end of a straight uniform 1m long bar is pivoted on…

One end of a straight uniform 1m long bar is pivoted on horizontal table. It is released from rest when it makes an angle 30º from the horizontal (see figure). Its angular speed when it hits the table is given as n\sqrt n s-1, where n is an integer. The value of n is _________. JEE Main 2020 (Online) 9th January Morning Slot Physics - Rotational Motion Question 137 English

Step-by-Step Verified Solution

By energy conservation

Ui + Ki = Uf + Kf

⇒\Rightarrow mgl2sin⁡30∘mg{l \over 2}\sin 30^\circ + 0 = 0 + 12Iω2{1 \over 2}I{\omega ^2}

⇒\Rightarrow mg12×12mg{1 \over 2} \times {1 \over 2} = 12×m(1)23ω2{1 \over 2} \times {{m{{\left( 1 \right)}^2}} \over 3}{\omega ^2}

⇒\Rightarrow ω2=3g2{\omega ^2} = {{3g} \over 2}

⇒\Rightarrow ω=15\omega = \sqrt {15}

∴\therefore n = 15

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