A plank of mass $M$ and length $L$ is hinged at its mid point from a fixed support in vertical plane as shown. Plank is free to rotate in vertical plane about the hinge. Two persons of equal mass running on the plank with same speed v relative to the plank so that angular velocity $ω$ of the plank remains constant.Initially one person is at the centre of the plank and the other person is at a distance d from the first person . Assuming they run till running is possible then $v$ is

see full answer

Start JEE / NEET / Foundation preparation at rupees 99/day !!

21% of IItians & 23% of AIIMS delhi doctors are from Sri Chaitanya institute !!

An Intiative by Sri Chaitanya

independent of the separation between the persons.

independent of their mass

independent of the distance of the persons from the hinge.

a constant

answer is 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

$\begin{array}{rcl} m g [x \cos ω t + (x + d) \cos ω t] & = & ω \frac{d I}{d t} \\ \Rightarrow & m g \cos ω t (2 x + d) = ω \frac{d}{d t} [\frac{M L^{2}}{12} + m x^{2} + m {(x + d)}^{2}] \\ = & m ω [2 x v + 2 (x + d) v] \\ = & 2 m ω (2 x + d) v \\ \Rightarrow & v = \frac{g \cos ω t}{2 ω} \end{array}$

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

How to Join IIT after 10th

🔥 Start Your JEE/NEET Prep at Just ₹1999 / month - Limited Offer! Check Now!

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

How to Join IIT after 10th