A 14.5 kg mass, fastened to the end of a steel wire of unstretched length 1.0 m, is whirled in a vertical circle with an angular velocity of 2 rev/s at the bottom of the circle. The cross-sectional area of the wire is 0.065 . The elongation of the wire when the mass is at the lowest point of its path is:
What is the density of water at a depth where pressure is 80.0 atm, given that its density
at the surface is 1.03× ?
The volume contraction of a solid copper cube, 10 cm on an edge, when
subjected to a hydraulic pressure of 7.0× is:
(Bulk modulus of copper is .)
How much should the pressure on a litre of water be changed to compress it by 0.10%?
(Given Bulk modulus of water, )
Anvils made of single crystals of diamond, with the shape as shown in the figure, are used to investigate the 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?
A rod of length 1.05 m having negligible mass is supported at its ends by two wires of steel (wire A) and aluminium (wire B) of equal lengths as shown in the figure. The cross-sectional areas of wires A and B are 1.0 and 2.0 , respectively. At what point along the rod should a mass m be suspended in order to produce equal stresses in both steel and aluminium wires?
1. 0.7 m from wire A
2. 0.07 m from wire A
3. 7.0 m from wire A
4. 0.007 m from wire A
Two strips of metal are riveted together at their ends by four rivets, each of diameter 6.0 mm. What is the maximum tension that can be exerted by the riveted strip if the shearing stress on the rivet is not to exceed 6.9× Pa? (Assume that each rivet is to carry one-quarter of the load.)
(1) 7850 N
(2) 6000 N
(3) 7070.73 N
(4) 7799.76 N
The Marina trench is located in the Pacific Ocean, and at one place it is nearly eleven km beneath the surface of the water. The water pressure at the bottom of the trench is about 1.1 × Pa. A steel ball of initial volume 0.32 is dropped into the ocean and falls to the bottom of the trench. What is the change in the volume of the ball when it reaches the bottom? [Given:]
A steel cable with a radius of 1.5 cm supports a chairlift at a ski area. If the maximum stress is not to exceed 108 N/m2, what is the maximum load that the cable can support?
1. 7.06 x 104 N
2. 5.03 x 104 N
3. 1.09 x 104 N
4. 17 x 104 N
Four identical hollow cylindrical columns of mild steel support a big structure of a mass of 50,000 kg. The inner and outer radii of each column are 30 cm and 60 cm respectively. Assuming the load distribution to be uniform, the compressional strain of each column is:
(Given, Young's modulus of steel, )