71. A large tank filled with water to a height $$'h'$$ is to be emptied through a small hole at the bottom. The ratio of time taken for the level of water to fall from $$h$$ to $$\frac{h}{2}$$ and $$\frac{h}{2}$$ to zero is
A
$$\sqrt 2 $$
B
$$\frac{1}{{\sqrt 2 }}$$
C
$$\sqrt 2 - 1$$
D
$$\frac{1}{{\sqrt 2 - 1}}$$
Answer :
$$\sqrt 2 - 1$$
72. When a pressure of $$100$$ atmosphere is applied on a spherical ball, then its volume reduces to $$0.01\% .$$ The bulk modulus of the material of the rubber in $$dyne/c{m^2}$$ is
A
$$10 \times {10^{12}}$$
B
$$100 \times {10^{12}}$$
C
$$1 \times {10^{12}}$$
D
$$10 \times {10^{ - 12}}$$
Answer :
$$1 \times {10^{12}}$$
73. The bulk modulus of a spherical object is $$'B'.$$ If it is subjected to uniform pressure $$'p',$$ the fractional decrease in radius is
A
$$\frac{B}{{3p}}$$
B
$$\frac{{3p}}{B}$$
C
$$\frac{p}{{3B}}$$
D
$$\frac{p}{{B}}$$
Answer :
$$\frac{p}{{3B}}$$
74. A thick rope of density $$\rho $$ and length $$L$$ is hung from a rigid support. The Young’s modulus of the material of rope is $$Y.$$ The increase in length of the rope due to its own weight is
A
$$\frac{{\left( {\frac{1}{4}} \right)\rho g{L^2}}}{Y}$$
B
$$\frac{{\left( {\frac{1}{2}} \right)\rho g{L^2}}}{Y}$$
C
$$\frac{{\rho g{L^2}}}{Y}$$
D
$$\frac{{\rho gL}}{Y}$$
Answer :
$$\frac{{\left( {\frac{1}{2}} \right)\rho g{L^2}}}{Y}$$
75.
A hollow wooden cylinder of height $$h,$$ inner radius $$R$$ and outer radius $$2R$$ is placed in a cylindrical container of radius $$3R.$$ When water is poured into the container, the minimum height $$H$$ of the container for which cylinder can float inside freely is
A
$$\frac{{h{\rho _{{\text{water}}}}}}{{{\rho _{{\text{water}}}} + {\rho _{{\text{wood}}}}}}$$
B
$$\frac{{h{\rho _{{\text{wood}}}}}}{{{\rho _{{\text{water}}}}}}$$
C
$$h$$
D
$$\frac{{{h^2}}}{R}$$
Answer :
$$\frac{{h{\rho _{{\text{wood}}}}}}{{{\rho _{{\text{water}}}}}}$$
76. If the length of a wire is reduced to half, then it can hold the
A
half load
B
same load
C
double load
D
one fourth load
Answer :
same load
77. A spherical ball of iron of radius $$2\,mm$$ is falling through a column of glycerine. If densities of glycerine and iron are respectively $$1.3 \times {10^3}\,kg/{m^3}$$ and $$8 \times {10^3}\,kg/{m^3}.\eta $$ for glycerine $$ = 0.83\,N{m^{ - 2}}\sec ,$$ then the terminal velocity is
A
$$0.7\,m/s$$
B
$$0.07\,m/s$$
C
$$0.007\,m/s$$
D
$$0.0007\,m/s$$
Answer :
$$0.07\,m/s$$
78. Which of the following is the correct relation? $$Y = $$ Young's modulus & $$G =$$ modulus of rigidity?
A
$$Y < G$$
B
$$Y > G$$
C
$$Y = G$$
D
None of these
Answer :
$$Y > G$$
79. If the terminal speed of a sphere of gold (density $$ = 19.5\,kg/{m^3}$$ ) is $$0.2 \,m/s$$ in a viscous liquid (density $$ = 1.5\,kg/{m^3}$$ ), find the terminal speed of a sphere of silver (density $$ = 10.5\,kg/{m^3}$$ ) of the same size in the same liquid-
A
$$0.4\,m/s$$
B
$$0.133\,m/s$$
C
$$0.1\,m/s$$
D
$$0.2\,m/s$$
Answer :
$$0.1\,m/s$$
80. A uniform cylinder of length $$L$$ and mass $$M$$ having cross-sectional area $$A$$ is suspended, with its length vertical, from a fixed point by a massless spring such that it is half submerged in a liquid of density $$\sigma $$ at equilibrium position. The extension $${x_0}$$ of the spring when it is in equilibrium is:
A
$$\frac{{Mg}}{k}$$
B
$$\frac{{Mg}}{k}\left( {1 - \frac{{LA\sigma }}{M}} \right)$$
C
$$\frac{{Mg}}{k}\left( {1 - \frac{{LA\sigma }}{{2M}}} \right)$$
D
$$\frac{{Mg}}{k}\left( {1 + \frac{{LA\sigma }}{M}} \right)$$
Answer :
$$\frac{{Mg}}{k}\left( {1 - \frac{{LA\sigma }}{{2M}}} \right)$$
