A bob of mass , suspended by a string of length , 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 suspended by a string of length , which is init

Question

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 massless and inextensible. If the second bob, after collision, acquires the minimum speed required to complete a full circle in the vertical plane, the ratio $\frac{l_{1}}{l_{2}}$ is [2013]

Smart Achievers · Accepted Answer

(5)

Due to elastic head-on collision of equal mass $l_{1}$ of bob, velocity at the highest point of bob tied to string $ℓ_{1}$ is acquired by the bob tied to string $l_{2}$ .

$∴$ $\sqrt{g ℓ_{1}} = \sqrt{5 g ℓ_{2}} \Rightarrow \frac{ℓ_{1}}{ℓ_{2}} = 5$

Solution

Ans.
(5)

Due to elastic head-on collision of equal mass $m$ of bob, velocity at the highest point of bob tied to string $ℓ_{1}$ is acquired by the bob tied to string $ℓ_{2}$ .

$∴$ $\sqrt{g ℓ_{1}} = \sqrt{5 g ℓ_{2}} \Rightarrow \frac{ℓ_{1}}{ℓ_{2}} = 5$

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Solution

Ans. (5) Due to elastic head-on collision of equal mass m of bob, velocity at the highest point of bob tied to string ℓ1 is acquired by the bob tied to string ℓ2. ∴ gℓ1=5gℓ2 ⇒ ℓ1ℓ2=5

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Ans.
(5)

Due to elastic head-on collision of equal mass $m$ of bob, velocity at the highest point of bob tied to string $ℓ_{1}$ is acquired by the bob tied to string $ℓ_{2}$ .

$∴$ $\sqrt{g ℓ_{1}} = \sqrt{5 g ℓ_{2}} \Rightarrow \frac{ℓ_{1}}{ℓ_{2}} = 5$