1. Identify the type of collision

A bullet gets embedded in the sand bag, so this is a perfectly inelastic collision.

Thus, momentum is conserved, but kinetic energy is not conserved.

2. Given data

• Mass of bag: $m_1 = 9.8\,\text{kg}$
• Mass of bullet: $m_2 = 200\,\text{g} = 0.2\,\text{kg}$
• Speed of bullet before collision: $u_2 = 10\,\text{m s}^{-1}$
• Bag is initially at rest: $u_1 = 0$

3. Find common velocity after collision

Using conservation of linear momentum:

$m_1u_1 + m_2u_2 = (m_1+m_2)v$

Substitute values:

$9.8(0) + 0.2(10) = (9.8+0.2)v$

$2 = 10v$

$v = 0.2\,\text{m s}^{-1}$

4. Initial kinetic energy

Only the bullet is moving initially:

$K_i = \frac{1}{2}m_2u_2^2$

$K_i = \frac{1}{2}(0.2)(10)^2$

$K_i = 0.1 \times 100 = 10\,\text{J}$

5. Final kinetic energy

After collision, combined mass moves with speed $0.2\,\text{m s}^{-1}$:

$K_f = \frac{1}{2}(m_1+m_2)v^2$

$K_f = \frac{1}{2}(10)(0.2)^2$

$K_f = 5 \times 0.04 = 0.2\,\text{J}$

6. Loss of kinetic energy

$\Delta K = K_i - K_f$

$\Delta K = 10 - 0.2 = 9.8\,\text{J}$

7. Check options

• A: $4.9\,\text{J}$
• B: $9.8\,\text{J}$
• C: $14.7\,\text{J}$
• D: $19.6\,\text{J}$

So the correct option is:

$\boxed{\text{B }(9.8\,\text{J})}$

8. Comparison with stored correct answer

Stored correct answer: B

Our derived answer: B

They match.