Three particle A, B, C mass m, $2$ m & m are connected with the cup of massless rod of length l. Rod can rotate freely about c. Sys. released from rest when rod almost vertical. A & B start moving in opposite direction. Find displacement of C when it list the ground.

Open in App

Solution

Let the system is at vertical in figure.The centre of mass is along line shown in figure let $x$ co-ordinate of com is at 0.Find position of ABC are given in figure b.Let $x$ be the displacement from their initial point..
$x = \frac{2 m (l - x) - m x - m (l - x)}{4 m} = 0 2 (l - x) - x - l + x = 0 2 l - 2 x - x - l + x = 0 l - 2 x = 0 x = \frac{l}{2}$

Suggest Corrections

Similar questions

Q. A uniform rod of mass

m

and length

L

is hinged about one end and can freely rotate in a vertical plane. The angular velocity of the rod, when it falls from position

P

P

through an angle

α

starting from rest, is:

In the figure shown the cart of mass '6m' is initially at rest. A particle of mass 'm' is attached to the end of the light rod which can rotate freely about A. If the rod is released from rest in a horizontal position shown, determine the velocity $v_{r e l}$ of the particle with respect to the cart when the rod is vertical.