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Q.

A mass of 0.98 Kg suspended using a spring of constant K = 300Nm^-1 is hit by a bullet of 20 gm moving with a velocity 3 m/s vertically. The bullet gets embedded and oscillates with the mass. The amplitude of oscillation will be

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a

0.15 cm

b

0.12 cm

c

0.34 cm

d

12 cm

answer is C.

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Detailed Solution

LCLM $mv = (m + M) V = (m + M) Aω$
$\begin{array}{l} m + M = 20 \times 10^{- 3} + 0 .98 = 1 kg; \\ ω = \sqrt{\frac{K}{m}} = \sqrt{\frac{300}{1}} \\ = \sqrt{3} \times 10 \\ 20 \times 10^{- 3} \times 3 = 1 \times A \times \sqrt{3} \times 10 \\ A = 2 \sqrt{3} \times 10^{- 3} = 0 .34 cm \end{array}$

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A mass of 0.98 Kg suspended using a spring of constant K = 300Nm-1 is hit by a bullet of 20 gm moving with a velocity 3 m/s vertically. The bullet gets embedded and oscillates with the mass. The amplitude of oscillation will be