Question

A rod of negligible mass and length l is pivoted
at its centre. A particle of mass m is fixed to its
left end & another particle of mass 2 m is fixed to
the right end. If the system is released from rest,
m
pivot
2m
(a) what is the speed v of the two masses when
the rod is vertical.
(b) what is the angular speed o of the system at
that instant​

Answer 1

Answer:

speed is equal for each = 2g/l , angular speed g

Explanation:

Using torque Equation,

m(l/2)^2v = mg( l/2)Sina when the rod tilted by angle a

or, v = 2g /l ( Sina) or v = 2g/l since Sin90 degree =1

For the other mass 2m,

2m(l/2)^2u = 2mg( l/2) Sin a

or u = 2g/l putting a = 90 degree.

Their angular speeds are 2g/l ÷ l/2 = g

this is independent of m.

Hence (a) 2g/l for both particles

(b) g for both particles.