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}
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 10^{3} kg/m^{3 }and its Young’s modulus is 9.27 x 10^{10} 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 10^{10} N/m^{2}, 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.
2 mm
Given, r_{1} : r_{2} = 1 : 2 and l_{1} = 8
In the first condition (cross-section area)
${\mathrm{A}}_{1}={{\mathrm{\pi r}}_{1}}^{2}.......\left(\mathrm{i}\right)$
In the second condition (cross-section area)
${\mathrm{A}}_{2}={{\mathrm{\pi r}}_{2}}^{2}........\left(\mathrm{ii}\right)$
On dividing Eq. (i) by Eq. (ii), we get
$\frac{{\mathrm{A}}_{1}}{{\mathrm{A}}_{2}}=\frac{{{\mathrm{r}}_{1}}^{2}}{{{\mathrm{r}}_{2}}^{2}}\mathrm{or}\frac{{\mathrm{A}}_{1}}{{\mathrm{A}}_{2}}={\left(\frac{1}{2}\right)}^{2}=\frac{1}{4}$
Stress_{1} : Stress_{2} = 4 : 1
Strain_{1} : Strain_{2} = 4 : 1
$\frac{{\mathrm{l}}_{1}}{{\mathrm{l}}_{2}}=\frac{4}{1}\Rightarrow {\mathrm{l}}_{1}=4{\mathrm{l}}_{2}$
Increase in length of B,
${\mathrm{l}}_{2}=\frac{{\mathrm{l}}_{1}}{\mathrm{n}}=\frac{8}{2}\phantom{\rule{0ex}{0ex}}=2\mathrm{mm}$
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 × 10^{9}
9.8 × 10^{10}
1.96 × 10^{9}
9.8 × 10^{11}
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