Determine the volume contraction of a solid copper cube, 10 cm on an edge, when subjected to a hydraulic pressure of 7.0 ×106 Pa.
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Explanation:
Length of an edge of the solid copper cube, l = 10 cm = 0.1 m
Hydraulic pressure, p = 7.0 × 106 Pa
Bulk modulus of copper, B = 140 × 109 Pa
Bulk modulus, B = p / (∆V/V)
Where,
∆V/V = Volumetric strain
ΔV = Change in volume
V = Original volume.
ΔV = pV / B
Original volume of the cube, V = l3
∴ ΔV = pl3 / B
= 7 × 106 × (0.1)3 / (140 × 109)
= 5 × 10-8 m3 = 5 × 10-2 cm-3
Therefore, the volume contraction of the solid copper cube is 5 × 10–2 cm–3.
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ʜᴇʏᴀ..
ʜᴇʀᴇ ɪs ᴜʀ ᴀɴsᴡᴇʀ
ᴇᴀᴄʜ sɪᴅᴇ ᴏғ ᴄᴜʙᴇ (ʟ) = 10ᴄᴍ
= 0.1 ᴍ
ʜʏᴅʀᴀᴜʟɪᴄ ᴘʀᴇssᴜʀᴇ (ᴘ) = 7×10^6 ɴ/ᴍ²
ʙᴜʟᴋ ᴍᴏᴅᴜʟᴜs ( ᴋ) =140×10^9ᴘᴀ
ᴠᴏʟᴜᴍᴇ ᴄᴏɴᴛʀᴀᴄᴛɪᴏɴ (∆ᴠ) = ?
ʙᴜʟᴋ ᴍᴏᴅᴜʟᴜs ( ᴋ) = ∆ᴘ/{∆ᴠ/ᴠ}
∆ᴠ = ᴘᴠ/ᴋ
= 7× 10^6 × (0.1)³/140×10^9
= 0.05 × 10^-6 ᴍ³
= 5 × 10^-8 ᴍ³
i hope its help u
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