Question

Two beads 1 and 2 are allowed to descend on frictionless chord OA and vertical diameter OB of a circle , at the same instant from point O. The ratio of the velocities of the particles 1 and 2 respectively, when they reach on the circumference will be

(1) sin a
(2) tan a
(3) cos a
(4) None of these

Answer 1

The ratio of the velocities of the beads 1 and 2 when they reach the circumference of the circle will be None of these. Hence, the correct answer is option (4).

Step-by-step explanation:

When two objects are allowed to descend on different paths from a common point, the ratio of their velocities when they reach the circumference of a circle depends on the ratio of their initial heights and the radius of the circle.

Let's assume that the height of object 1 (bead 1) is h1 and the height of object 2 (bead 2) is h2. The ratio of their velocities when they reach the circumference will be given by:

Velocity ratio = √(2gh1) / √(2gh2)

We can see that the radius of the circle (OB) does not affect the velocity ratio.

So, the answer is (4) None of these.