In a circket match, batsman hit the ball (mass = m) high in the air and fielding side player catch the ball near boundary. De Broglie wavelength of ball just after hit from bat is $λ_{1}$ and just before the catch is $λ_{2}$ . Assume height at which ball is hit by bat and height at which ball is catch are same. Find total work done by air-resistance (Mechanical) energy is loss only due to air-resistance)

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$\frac{h^{2}}{m} (\frac{1}{λ_{1}} - \frac{1}{λ_{2}})$

$\frac{h^{2}}{2 m} (\frac{λ_{1} λ_{2}}{λ_{1} - λ_{2}})$

$\frac{h^{2}}{2 m} (\frac{1}{λ_{1}} - \frac{1}{- λ_{2}})$

$\frac{h^{2}}{2 m} (\frac{1}{λ_{1}^{2}} - \frac{1}{λ_{2}^{2}})$

answer is B.

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Detailed Solution

Kinetic energy of ball $= \frac{h^{2}}{2 m λ^{2}}$
Loss in kinetic energy $= \frac{h^{2}}{2 m} (\frac{1}{λ_{1}^{2}} - \frac{1}{λ_{2}^{2}})$

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