Bob $B$ of mass $m$ at rest is hanging vertically from the ceiling via a massless string of length 1

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Bob $B$ of mass $m$ at rest is hanging vertically from the ceiling via a massless string of length 10 m, as shown in the figure. Point mass $A$ of mass $m$ travelling horizontally with speed $10{\text{ }ms}^{- 1}$ hits bob $B$ elastically. The bob $B$ rises $h$ meter after the collision. Taking the acceleration due to gravity $g = 10{\text{ }ms}^{- 2}$ and neglecting the size of the bob, the value of $h$ is:

Accepted Answer

Sol. [Key Concept: Conservation of momentum and energy in a collision] • To reach the horizontal position, velocity of bob should be $= 10\sqrt{2}	ext{ }m/s$- Velocity of bob and point mass will be interchanged after elastic collision By conservation of energy$$\begin{matrix} & mgh = \frac{1}{2}mv^{2} \ & h = \frac{v^{2}}{2g} \ & h = \frac{(10)^{2}}{2 	imes 10} \ & h = 5	ext{ }m \end{matrix}$$

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