A small bob A of mass m is attached to a massless rigid rod of length 1 m pivoted at point P and kept at an angle of 60° with the vertical as shown in the figure. [2026]

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Solution

Q.
A small bob A of mass m is attached to a massless rigid rod of length 1 m pivoted at point P and kept at an angle of 60° with the vertical as shown in the figure. At a distance of 1 m below point P, an identical bob B is kept at rest on a smooth horizontal surface that extends to a circular track of radius R as shown in the figure. If bob B just manages to complete the circular path of radius R up to a point Q after being hit elastically by bob A, then the radius R is ______ m. [2026]

1 $\frac{1}{5}$

2 $\frac{3}{5}$

3 $\frac{2 + \sqrt{3}}{5}$

4 $\frac{2 - \sqrt{3}}{5}$

Ans.
(1)

$V_{A} at lowest point$

$V_{A} = \sqrt{2 g l (1 - \cos θ)}$

$V_{A} = \sqrt{2 \times 10 \times 1 (1 - \frac{1}{2})} = \sqrt{10}$

$After collision velocity of B becomes,$

$V_{A} = \sqrt{10} = V_{B} (Same mass)$

$Now to complete circular motion$

$V_{B} = \sqrt{5 g R}$

$R = \frac{1}{5}$

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