Question

Physics question.
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Give answer with proper explanation.

Answer 1

Given Information,

• Mass of the sand bag is M.
• Mass of the bullet is m.
• Velocity of the bullet is v.

Initially the sand bag is at rest, thus initial KE of the system is 1/2mv².

Now, in accordance with Law of conversation of Linear Momentum.

mv = (M + m)V

$\longrightarrow$ V = mv/(m + M)

KE of the system now would be :

K = 1/2mV²

$\longrightarrow$ K = 1/2(m + M)(mv/m + M)²

Now, for loss in KE :

$\longrightarrow$ Initial KE - Final KE

$\longrightarrow$ 1/2mv² - 1/2(mv)²/(m + M)

$\longrightarrow$ 1/2mv²[1 - (m/M + m)]

$\longrightarrow$ 1/2mv²[M + m - m/(m + M)]

$\longrightarrow$ Mmv²/2(M + m)

Option (A) is correct.