Mechanical Properties of Solids

One solid sphere A and another hollow sphere B are of same mass and same outer radii. Their moment of inertia about their diameters are respectively I_A and I_B such that


Where d_A and d_B are their densities.

• I_A = I_B

• I_A > I_B

• I_A < I_B

• I_A < I_B

What would be the work done in stretching a wire.

A granite rod of 60 cm length is clamped at its middle point and is set into longitudinal vibrations. The density of granite is 2.7 x 10³ kg/m³ and its Young’s modulus is 9.27 x 10¹⁰ Pa. What will be the fundamental frequency of the longitudinal vibrations?

• 7.5 kHz

• 5 kHz

• 2.5 kHz

• 10 kHz

The density of a material in the shape of a cube is determined by measuring three sides of the cube and its mass. If the relative errors in measuring the mass and length are respectively 1.5% and 1%, the maximum error in determining the density is:

• 6%

• 2.5%

• 3.5%

• 4.5%

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 the area a floats on the surface of the liquid, covering an entire cross section of 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, (dr/r), is

• mg/Ka

• Ka/mg

• Ka/3mg

• mg/3Ka

Which of the following statement related to stress-strain relation is correct ?

• Stress is linearly proportional to strain irrespective of the magnitude of the strain

• Stress is linearly proportional to strain above

• Stress is linearly proportional to strain for stress much smaller than at the yield point

• Stress-strain curve is same for all materials

The lower edge of a square slab of side 50 cm and thickness 20 cm is rigidly fixed to the base of a table. A tangential force of 30 N is applied to the slab. If the shear moduli of the material is 4 x 10¹⁰ N/m², then displacement of the upper edge, in meters is

• 4 × 10^-12

• 4 × 10^-10

• 6 × 10^-10

• 6 × 10^-12

Two wires A and B of same material and of equal length with the radii in the ratio 1 : 2 are subjected to identical loads. If the lengthof A increases by 8 mm, then the  increase in length of B is

• 2 mm

• 4 mm

• 8 mm

• 16 mm

A ball falling in a lake of depth 400 m has a decrease of 0.2% in its volume at the bottom. The bulk modulus of the material of the ball is (in Nm^-2)

• 9.8 × 10⁹

• 9.8 × 10¹⁰

• 1.96 × 10⁹

• 9.8 × 10¹¹

A steel plate of size 6 cm x 6 cm is to be coated by a metal on both sides with a coating thickness of 0.1 mm by electrolysis. If the density and ece of the metal are respectively 10 g cm^-3 and 0.001 gC^-1 then the strength of the current to complete the process in one hour is

• 1 A

• 0.5 A

• 6 A

• 2 A