Question

A rod of mass m and length l = 50/3 m is hinged in a plank of same mass m. the plank is kept on a smooth horizontal surface and the rod makes an angle theta with the vertical . the system is released from theta = 0 degree find the velocity of the plank when the rod makes an angle theta = 180 degree?

Answer 1

Given:

Mass of the rod = m

Mass of the plank = m

Length of the rod = 50/3m

To find:

Velocity of the plank when the rod makes an angle of theta = 180°

Solution:

When the rod makes an angle 0 degrees then the initial velocity and when it makes 180 degrees the vertical velocity will be u.

The center of mass of the rod will be at centre of the rod.

1/2mu^2 +  1/2 mu^2 = 2mgl/2

v = (2gl)^(-2)

Putting the value of l:

v= (2*9.8*50/3)^(-2)

v= 18 m/s

Therefore, the velocity when the rod makes 180 degrees is 18 m/s.