Question

A weightless rod of length 2l carries two equal masses 'm', one tied at lower end A and the other at the middle of the rod at B. The rod can rotates in vertical plane about a fixed axis passing though C. The rod is released from rest in horizontal position. The speed of mass B at the instant , rod become vertical is
(1)square(3gl/5)
(2)square(4gl/5)
(3)square(6gl/5)
(4)square(7gl/5)

Answer 1

Answer on Question #49832- Physics-Mechanics-Kinematics-Dynamics

A weightless rod of length 2l carries two equal masses 'm', one tied at lower end A and the other at the middle of the rod at B. The rod can rotates in vertical plane about a fixed axis passing though C. The rod is released from rest in horizontal position. The speed of mass B at the instant, rod become vertical is

(1) square(3gl/5)

(2) square(4gl/5)

(3) square(6gl/5)

(4) square(7gl/5)

Solution

According to the conservation of energy law:

$$P _ {i} = K _ {f} \rightarrow m g l + m g (2 l) = \frac {m v _ {B} ^ {2}}{2} + \frac {m v _ {A} ^ {2}}{2}.$$

The road rotates at some angular speed, when it became vertical:

$$\omega = \frac {v _ {B}}{l} = \frac {v _ {A}}{2 l} \rightarrow v _ {A} = 2 v _ {B}.$$

Thus,

$$3 m g l = \frac {m v _ {B} ^ {2}}{2} + \frac {m (2 v _ {B}) ^ {2}}{2} \rightarrow v _ {B} = \sqrt {\frac {6 g l}{5}}.$$

Answer: (3) $\sqrt{\frac{6gl}{5}}$