Let's solve both questions step by step. --- ## **Question 1** **In single point cutting tool, Negative rake angle:** - Improves machinability - None of the above - Improves strength of the cutting tool - Both A and B ### **Explanation** - **Negative rake angle** generally improves the **strength of the cutting tool** because it provides more material behind the cutting edge, making it stronger and more durable. - However, it does **not improve machinability**—in fact, it usually decreases machinability (makes cutting harder). ### **Correct Option** - **Improves strength of the cutting tool** So, the correct option is: > **Improves strength of the cutting tool** --- ## **Question 2** ### **Given:** - BCC structure (Body Centered Cubic) - Atomic weight = **167.5 g/mol** - Density = **12.5 g/cm³** ### **To Find:** Radius of the atom --- ### **Step 1: Relationship for BCC structure** For BCC: - Number of atoms/unit cell = 2 - Volume of unit cell = \( a^3 \) - Mass of unit cell = \( 2 \times \text{mass of 1 atom} \) - Density (\( \rho \)) = \(\frac{\text{Mass of unit cell}}{\text{Volume of unit cell}}\) #### **Mass of one atom:** \[ \text{Mass of one atom} = \frac{\text{Atomic weight}}{N_A} \] where \(N_A = 6.022 \times 10^{23}\) (Avogadro's number) #### **Density equation:** \[ \rho = \frac{2 \times \frac{\text{Atomic weight}}{N_A}}{a^3} \] \[ a^3 = \frac{2 \times \frac{\text{Atomic weight}}{N_A}}{\rho} \] --- ### **Step 2: Plug in values** \[ a^3 = \frac{2 \times \frac{167.5}{6.022 \times 10^{23}}}{12.5} \] Calculate numerator: \[ 2 \times 167.5 = 335 \] \[ \frac{335}{6.022 \times 10^{23}} = 5.563 \times 10^{-22} \] \[ a^3 = \frac{5.563 \times 10^{-22}}{12.5} = 4.45 \times 10^{-23} \text{cm}^3 \] \[ a = (4.45 \times 10^{-23})^{1/3} \approx 3.56 \times 10^{-8} \text{cm} = 0.356 \text{nm} \] --- ### **Step 3: Relate \(a\) and atomic radius (\(r\)) in BCC** For BCC: \[ a = \frac{4r}{\sqrt{3}} \] \[ r = \frac{a \sqrt{3}}{4} \] \[ r = \frac{0.356 \times 1.732}{4} \approx \frac{0.616}{4} = 0.154 \text{nm} \] --- ### **Match with options:** - 0.183 nm - **0.153 nm** - 0.143 nm - 0.123 nm ### **Correct Option** > **0.153 nm** --- ## **Summary Table** | Q# | Correct Option | |----|---------------| | 1 | Improves strength of the cutting tool | | 2 | 0.153 nm | --- Let me know if you need further explanation!