Question

Physics question.
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Give answer with proper explanation.​

Answer 1

$\huge\bold{Answer}$

Given Information,

• Mass of the sand bag M.
• Mass of the bullet is M.
• Velocity is the bullet is V.

Initially the sand bag is at rest, thus

initially KE of the system is 1/2mv².

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

mv = (M + m)V

⟶ V = mv/(m + M)

KE of the system now would be :

K = 1/2mV²

⟶ K = 1/2(m + M)(mv + M)²

Now, for loss in KE :

⟶ Initial KE - Final KE

⟶ 1/2mv² - 1/2(mv)²/(m + M)

⟶ 1/2mv²[1 - (m/M +m)]

⟶ 1/2mv²[M + m - m/(m + M)]

⟶ Mmv²/2(M + m)

Option (A) is correct.

Hope it's helpful :)

Answer 2

$\huge\underline\mathfrak\pink{♡\:Answer\:♡}$

Given :

• Mass of the sand bag M.
• Mass of the bullet is M.
• Velocity is the bullet is V.

Initially the sand bag is at rest, thus

initially KE of the system is 1/2mv².

Solution :

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

mv = (M + m)V

⟶ V = mv/(m + M)

KE of the system now would be :

K = 1/2mV²

⟶ K = 1/2(m + M)(mv + M)²

Now, for loss in KE :

⟶ Initial KE - Final KE

⟶ 1/2mv² - 1/2(mv)²/(m + M)

⟶ 1/2mv²[1 - (m/M +m)]

⟶ 1/2mv²[M + m - m/(m + M)]

⟶ Mmv²/2(M + m)

Option (A) is correct.