QJEEM20Pha456: JEE Main 2020 Physics - Class 11 JEEM20Pha456 Solution: Consider a uniform rod of mass M = 4m and length ℓ pivoted…

Question

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Consider a uniform rod of mass M = 4m and length

ℓ

pivoted about its centre. A mass m moving with velocity v making angle

θ = \frac{π}{4}

to the rod's long axis collides with one end of the rod and sticks to it. The angular speed of the rod-mass system just after the collision is :

Accepted Answer

About hinge(O) net torque

τ

= 0

So angular momentum is conserved about hinge(O),

L_initial = L_final

m

(\frac{v}{\sqrt{2}}) (\frac{l}{2})

+ 0 =

[\frac{4 m l^{2}}{12} + m {(\frac{l}{2})}^{2}] ω

\Rightarrow

ω

=

\frac{3 \sqrt{2}}{7} \frac{v}{ℓ}

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