1. Tardigrade
  2. Question
  3. Physics
  4. A bob of mass m, suspended by a string of length l1 is given a minimum velocity required to complete a full circle in the vertical plane. At the highest point, it collides elastically with another bob of mass m suspended by a string of length l2, which is initially at rest. Both the strings are mass-less and inextensible. If the second bob, after collision acquires the minimum speed required to complete a full circle in the vertical plane, the ratio l1/l2 is

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Q. A bob of mass $m$, suspended by a string of length $l_1$ is given a minimum velocity required to complete a full circle in the vertical plane. At the highest point, it collides elastically with another bob of mass $m$ suspended by a string of length $l_2$, which is initially at rest. Both the strings are mass-less and inextensible. If the second bob, after collision acquires the minimum speed required to complete a full circle in the vertical plane, the ratio $l_1/l_2$ is

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Solution:

Velocity of the first bob at $A = \sqrt{5\,gl_{1}}$
Velocity of the first bob at $B =\sqrt{gl_{1}}$
another bob of same mass $m$ suspended by a string of length $l_2$ as shown in figure.
image
When two bodies of equal masses undergoes an elastic collision, their velocities are interchanged.
$\therefore $ Velocity of the second bob at $B = \sqrt{gl_{1}}$
But to complete the vertical circle, the velocity of the second bob at $B = \sqrt{5\,gl_{2}}$
$\therefore \sqrt{gl_{1}} = \sqrt{5\,gl_{2}}$ or $\frac{l_{1}}{l_{2}} = 5$