Question

1. Find the increase in pressure required to decrease the volume of a water sample by 0.01 %. Bulk modulus of water is 2.1 x 109 N/m2

2. A steel plate of face-area 4 cm2 and thickness 0.5 cm is fixed rigidly at the lower surface. A tangential force of 10 N is applied on the upper surface. Find the lateral displacement of the upper surface with respect to the lower surface. Rigidity modulus (shear modulus) of steel is 8.4 x 1010 N/m2.

Answer 1

1)

$$\Delta p=\frac{\Delta V}{V}B$$

$$\Delta p=(0.0001)(2.1 \cdot10^9)=2.1 \cdot10^5\ Pa$$

2)

$$x=\frac{Fl}{A\eta}$$

$$x=\frac{(10)(0.5\cdot 10^{-2})}{(4\cdot 10^{-4})(8.4\cdot 10^{10})}=1.5\cdot 10^{-9}\ m=1.5\ nm$$