1. Given data

• Mass of wooden bob: $M = 1\,\text{kg}$
• Mass of bullet: $m = 10^{-2}\,\text{kg} = 0.01\,\text{kg}$
• Speed of bullet: $u = 2\times 10^2 = 200\,\text{m/s}$
• Acceleration due to gravity: $g = 10\,\text{m/s}^2$

The bullet gets embedded in the bob, so this is a perfectly inelastic collision.

2. Find common velocity just after collision

During the collision, linear momentum is conserved:

$mu = (M+m)V$

Substitute values:

$0.01 \times 200 = (1 + 0.01)V$

$2 = 1.01V$

$V = \frac{2}{1.01} \approx 1.98\,\text{m/s}$

3. Convert kinetic energy into gravitational potential energy

After collision, the combined mass rises upward. Its kinetic energy converts into potential energy:

$\frac{1}{2}(M+m)V^2 = (M+m)gh$

Cancel $(M+m)$:

$\frac{1}{2}V^2 = gh$

$h = \frac{V^2}{2g}$

Substitute $V \approx 1.98\,\text{m/s}$ and $g=10$:

$h = \frac{(1.98)^2}{2\times 10}$

$h = \frac{3.9204}{20} \approx 0.196\,\text{m}$

$h \approx 0.20\,\text{m}$

4. Check options

• A: $0.20\,\text{m}$ ✅
• B: $0.40\,\text{m}$
• C: $0.30\,\text{m}$
• D: $0.35\,\text{m}$

So the correct option is A.

5. Comparison with stored answer

Stored correct answer: A

Our derived answer: A

They match.