- 1(current)
Q. No.A solid sphere of radius \(r\) made of a soft material of bulk modulus \(K\) is surrounded by a liquid in a cylindrical container. A massless piston of area \(a\) floats on the surface of the liquid, covering the entire cross-section of the cylindrical container. When a mass \(m\) is placed on the surface of the piston to compress the liquid, the fractional decrement in the radius of the sphere, \( \left (\frac{dr}{r} \right )\) is:
1. \(\frac{Ka}{mg}\)
2. \(\frac{Ka}{3mg}\)
3. \(\frac{mg}{3Ka}\)
4. \(\frac{mg}{Ka}\)
A cube of metal is subjected to a hydrostatic pressure of \(4~\text{GPa}\). The percentage change in the length of the side of the cube is close to: (Given bulk modulus of metal, \(B=8 \times 10^{10} ~\text{Pa}\))
1. \(5\)
2. \(20\)
3. \(0.6\)
4. \(1.67\)
The normal density of a material is \(\rho\) and its bulk modulus of elasticity is \(K\). The magnitude of the increase in the density of material when a pressure \(P\) is applied uniformly on all sides, will be:
| 1. | \(\dfrac{\rho K}{P}\) | 2. | \(\dfrac{\rho P}{K}\) |
| 3. | \(\dfrac{K}{P\rho}\) | 4. | \(\dfrac{PK}{\rho}\) |
1. \(3\times10^{8}\) Nm–2
2. \(9\times10^{8}\) Nm–2
3. \(6\times10^{8}\) Nm–2
4. \(12\times10^{8}\) Nm–2
1. \(30~\mu \text m\)
2. \(48~\mu \text m\)
3. \(16~\mu \text m\)
4. \(64~\mu \text m\)
1. \(5\)
2. \(4\)
3. \(6\)
4. \(10\)
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Q. No.
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