Let’s solve the first question step by step:

Problem Description: A bullet of 10 gm was shot with 1.5 km/s towards a wall of 10 cm thickness. The velocity of the bullet has become one-third after penetrating 4 cm.

Part (a): What amount of force did the bullet experience by the wall?

1. Known values:

   • Initial mass of bullet ($m$) = $10 \, \text{gm} = 0.01 \, \text{kg}$
   • Initial velocity ($u$) = $1.5 \, \text{km/s} = 1500 \, \text{m/s}$
   • Final velocity ($v$) after penetrating 4 cm = $\frac{1}{3} \times 1500 = 500 \, \text{m/s}$
   • Distance penetrated ($s$) = $4 \, \text{cm} = 0.04 \, \text{m}$

2. Apply equation of motion: Using the equation: $v^2 = u^2 + 2as$ Rearrange to solve for acceleration ($a$): $a = \frac{v^2 - u^2}{2s}$ Substituting the values: $a = \frac{(500)^2 - (1500)^2}{2 \times 0.04}$ $a = \frac{250000 - 2250000}{0.08}$ $a = \frac{-2000000}{0.08} = -25000000 \, \text{m/s}^2$

   The negative sign indicates deceleration.

3. Force experienced by the bullet: Using Newton's second law: $F = ma$ Substituting the values: $F = 0.01 \times (-25000000) = -250000 \, \text{N}$ The magnitude of the force is: $F = 250000 \, \text{N}$

Part (b): Is it possible to penetrate the wall completely? Explain mathematically.

1. Total thickness of the wall: $10 \, \text{cm} = 0.1 \, \text{m}$

2. Deceleration of the bullet ($a$) has already been calculated as $-25000000 \, \text{m/s}^2$.

3. Distance required for the bullet to stop: Using the equation of motion: $v^2 = u^2 + 2as$ When the bullet stops, $v = 0$. Solve for $s$: $0 = u^2 + 2as$ $s = -\frac{u^2}{2a}$ Substituting the values: $s = -\frac{(1500)^2}{2 \times -25000000}$ $s = \frac{2250000}{50000000} = 0.045 \, \text{m} = 4.5 \, \text{cm}$

   Since the bullet can only penetrate $4.5 \, \text{cm}$, which is less than the total thickness of the wall ($10 \, \text{cm}$), it is not possible for the bullet to penetrate the wall completely.

Final Answers:

(a) The force experienced by the bullet is $250,000 \, \text{N}$.
(b) No, it is not possible for the bullet to penetrate the wall completely, as it can only penetrate $4.5 \, \text{cm}$.

Would you like further clarification or step-by-step elaboration?

Related Questions:

1. What is the kinetic energy of the bullet before and after penetrating 4 cm?
2. How much work is done by the wall to stop the bullet?
3. What would the penetration distance be if the wall thickness were 6 cm?
4. Can we calculate the time it took for the bullet to decelerate over 4 cm?
5. How does the force experienced relate to the material properties of the wall?

Tip: Always convert units to SI before solving any physics problem for consistency.