# determine the volume contraction of a solid copper cube

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## 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.

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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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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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.

Open in App Solution

Length of an edge of the solid copper cube, = 10 cm = 0.1 m

Hydraulic pressure, = 7.0 ×106 Pa

Bulk modulus of copper, = 140 × 109 Pa

Where, = Volumetric strain

Δ = Change in volume

= Original volume.

Original volume of the cube, = 3

Therefore, the volume contraction of the solid copper cube is 5 × 10–2 cm–3.

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SIMILAR QUESTIONS

**Q.**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.

**Q.**Determine the volume contraction of a solid copper cube,

10 c m

on an edge, when subjected to a hydraulic pressure of

7.0 × 10 6 P a

. (Bulk modulus of copper,

B = 140 × 10 9 P a )

**Q.**Determine the volume contraction of a solid copper cube,

10 c m

on an edge, when subject to a hydraulic pressure of

7 × 10 6 P a . K for copper = 140 × 10 9 Pa.

**Q.**A solid copper cube of edge

10 cm

is subjected to a hydraulic pressure of

7 × 10 6 Pa

. If compressibility of copper is

1 140 GPa − 1

, then contraction in its volume will be

**Q.**A solid cube of copper of edge 10 cm subjected to a hydraulic pressure of 7 x

10 6

pascal. If Bulk modulus of copper is 140 GPa, then contraction in its volume will be:

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## Determine the volume contraction of a solid copper cube, 10 cm on an edge, when subjected to a hydraulic pressure of 7.0 × 10^6 Pa . (Bulk modulus of copper, B = 140 × 10^9Pa )

Click here👆to get an answer to your question ✍️ Determine the volume contraction of a solid copper cube, 10 cm on an edge, when subjected to a hydraulic pressure of 7.0 × 10^6 Pa . (Bulk modulus of copper, B = 140 × 10^9Pa )

Determine the volume contraction of a solid copper cube, 10 cm on an edge, when subjected to a hydraulic pressure of 7.0×10Question 6

Pa. (Bulk modulus of copper, B=140×10

9 Pa) Medium Open in App

Updated on : 2022-09-05

Using formulaSolution Verified by Toppr K=− V δV P We get δV=− K PV =− 140×10 9 7×10 6 ×0.001 =−0.05×10 −6 m 3 Video Explanation

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## 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.

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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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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### SOLUTION 1

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△VV Where △VV = Volumetric strain

ΔV = Change in volume

V = Original volume.

△V=pVB

Original volume of the cube,

V=β ∴△V=pl3B

=7×106×(0.1)3140×109

= 5 x 10-8 m3 = 5 x 10-2 cm-3

Therefore, the volume contraction of the solid copper cube is 5 × 10–2 cm–3.

### SOLUTION 2

Here a side of copper cube a = 10 cm, hence volume V = a3 = 10-3 m3 , hydraulic pressure applied p = 7.0 x 106 Pa and from table we find that bulk modulus of copper B = 140 G Pa = 140 x 109 Pa.

Using the relation B =p△VV

we have decreased in

volume △V =PVB

∴△V=7.0×106×10-3140×109=5×10-8m3=5×10-2cm3

Concept: Stress and Strain

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Chapter 9: Mechanical Properties of Solids - Exercises [Page 244]

Q 15 Q 14 Q 16

### APPEARS IN

NCERT Class 11 Physics

Chapter 9 Mechanical Properties of Solids

Exercises | Q 15 | Page 244

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