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Mechanical Properties Of Fluids

Question
CBSEENPH11019984

Anvils made of single crystals of diamond, with the shape as shown in Fig. 9.14, are used to investigate behaviour of materials under very high pressures. Flat faces at the narrow end of the anvil have a diameter of 0.50 mm, and the wide ends are subjected to a compressional force of 50,000 N. What is the pressure at the tip of the anvil?


Solution
Diameter of the cones at the narrow ends, d = 0.50 mm = 0.5 × 10–3 m
Radius, r = d/2  =  0.25 × 10-3 m 
Compressional force, F = 50000 N\
Pressure at the tip of the anvil is given by, 

straight P space space equals space straight F over straight A equals space fraction numerator 50000 over denominator straight pi space left parenthesis 0.25 cross times 10 to the power of negative 3 end exponent right parenthesis squared end fraction space

space space space space equals space 2.55 cross times 10 to the power of 11 space Pa space
Therefore, the pressure at the tip of the anvil is 2.55 × 1011Pa.