A thin uniform rod of mass m and l length is free to rotate about its upper end. When it is at rest, it receives an impulse J at its lowest point, normal to its length. Immediately, after impact

see full answer

Want to Fund your own JEE / NEET / Foundation preparation ??

Take the SCORE scholarship exam from home and compete for scholarships worth ₹1 crore!*

An Intiative by Sri Chaitanya

The angular momentum of rod is $J l$

The angular velocity of rod is $\frac{3 J}{m l}$

The kinetic energy of rod is $\frac{3 J^{2}}{2 m}$

The linear velocity of mid point of rod is $\frac{3 J}{2 m}$

answer is A, B, C, D.

(Unlock A.I Detailed Solution for FREE)

Ready to Test Your Skills?

Check your Performance Today with our Free Mock Test used by Toppers!

Take Free Test

Detailed Solution

About point of contact

$\begin{array}{r} L = (J) l . \dots \dots \dots . . (1) \\ Jl = (\frac{{ml}^{2}}{3}) ω \\ W = \frac{3 J}{ml} \dots \dots \dots (2) \\ K . E = \frac{1}{2} {Iω}^{2} = \frac{3 J^{2}}{2 m} . \end{array}$

And linear velocity of mid point of rod is given by

$ω \times \frac{l}{2} = \frac{3 J}{ml} \times \frac{l}{2} = \frac{3 J}{2 m}$

Watch 3-min video & get full concept clarity

Result Producing online coaching for JEE/NEET of south India

Largest All India Test Series for JEE/NEET

Best Books for IIT JEE

Best Books for NEET

Get Expert Academic Guidance – Connect with a Counselor Today!

Result Producing online coaching for JEE/NEET of south India

Largest All India Test Series for JEE/NEET

Best Books for IIT JEE

Best Books for NEET