01. Young's Modulus and Bulk Modulus and Change in Length
Mechanical Properties of Solids

140998 The compressibility of water is $6 \times 10^{-10} \mathrm{~N}^{-1} \mathrm{~m}^{2}$. If one litre is subjected to a pressure of $4 \times 10^{7} \mathrm{~N}$ $\mathrm{m}^{-2}$, the decrease in its volume is

1 $10 \mathrm{cc}$
2 $24 \mathrm{cc}$
3 $15 \mathrm{cc}$
4 $12 \mathrm{cc}$
Mechanical Properties of Solids

140999 A wire of length $L$ and cross-sectional area $A$ is made of a material with Young's modulus Y. If the wire is stretched by an amount $x$, the work done is

1 $\frac{\mathrm{YAx}^{2}}{2 \mathrm{~L}}$
2 $\frac{\mathrm{YAx}^{2}}{\mathrm{~L}}$
3 $\frac{Y A x}{2 L}$
4 $\mathrm{YAx}^{2} \mathrm{~L}$
Mechanical Properties of Solids

141000 A uniform cylindrical rod of length ' $L$ ' area of cross-section ' $A$ ' and Young's modulus ' $Y$ ' is acted upon by the forces as shown in the figure. The elongation of the rod is

1 $\frac{3 \mathrm{FL}}{5 \mathrm{AY}}$
2 $\frac{2 \mathrm{FL}}{5 \mathrm{AY}}$
3 $\frac{3 \mathrm{FL}}{8 \mathrm{AY}}$
4 $\frac{8 \mathrm{FL}}{3 \mathrm{AY}}$
Mechanical Properties of Solids

141001 A composite steel rod $P Q R$ is made of two rods $P Q$ and $Q R$ as shown in figure. The lengths of two rods $P Q$ and $Q R$ are $20 \mathrm{~cm}$ and $10 \mathrm{~cm}$ respectively. The area of cross-section of the longer rod is $2 \times 10^{-4} \mathrm{~m}^{2}$ and that of the shorter $\operatorname{rod}$ is $1 \times 10^{-4} \mathrm{~m}^{2}$. If the composite $\operatorname{rod}$ is stretched with a force of $50 \times 10^{3} \mathrm{~N}$, the total elongation produced is
(Young's modulus of steel $=20 \times 10^{10} \mathrm{Nm}^{-2}$ )

1 $5 \mathrm{~mm}$
2 $0.5 \mathrm{~mm}$
3 $25 \mathrm{~mm}$
4 $2.5 \mathrm{~mm}$
Mechanical Properties of Solids

140998 The compressibility of water is $6 \times 10^{-10} \mathrm{~N}^{-1} \mathrm{~m}^{2}$. If one litre is subjected to a pressure of $4 \times 10^{7} \mathrm{~N}$ $\mathrm{m}^{-2}$, the decrease in its volume is

1 $10 \mathrm{cc}$
2 $24 \mathrm{cc}$
3 $15 \mathrm{cc}$
4 $12 \mathrm{cc}$
Mechanical Properties of Solids

140999 A wire of length $L$ and cross-sectional area $A$ is made of a material with Young's modulus Y. If the wire is stretched by an amount $x$, the work done is

1 $\frac{\mathrm{YAx}^{2}}{2 \mathrm{~L}}$
2 $\frac{\mathrm{YAx}^{2}}{\mathrm{~L}}$
3 $\frac{Y A x}{2 L}$
4 $\mathrm{YAx}^{2} \mathrm{~L}$
Mechanical Properties of Solids

141000 A uniform cylindrical rod of length ' $L$ ' area of cross-section ' $A$ ' and Young's modulus ' $Y$ ' is acted upon by the forces as shown in the figure. The elongation of the rod is

1 $\frac{3 \mathrm{FL}}{5 \mathrm{AY}}$
2 $\frac{2 \mathrm{FL}}{5 \mathrm{AY}}$
3 $\frac{3 \mathrm{FL}}{8 \mathrm{AY}}$
4 $\frac{8 \mathrm{FL}}{3 \mathrm{AY}}$
Mechanical Properties of Solids

141001 A composite steel rod $P Q R$ is made of two rods $P Q$ and $Q R$ as shown in figure. The lengths of two rods $P Q$ and $Q R$ are $20 \mathrm{~cm}$ and $10 \mathrm{~cm}$ respectively. The area of cross-section of the longer rod is $2 \times 10^{-4} \mathrm{~m}^{2}$ and that of the shorter $\operatorname{rod}$ is $1 \times 10^{-4} \mathrm{~m}^{2}$. If the composite $\operatorname{rod}$ is stretched with a force of $50 \times 10^{3} \mathrm{~N}$, the total elongation produced is
(Young's modulus of steel $=20 \times 10^{10} \mathrm{Nm}^{-2}$ )

1 $5 \mathrm{~mm}$
2 $0.5 \mathrm{~mm}$
3 $25 \mathrm{~mm}$
4 $2.5 \mathrm{~mm}$
Mechanical Properties of Solids

140998 The compressibility of water is $6 \times 10^{-10} \mathrm{~N}^{-1} \mathrm{~m}^{2}$. If one litre is subjected to a pressure of $4 \times 10^{7} \mathrm{~N}$ $\mathrm{m}^{-2}$, the decrease in its volume is

1 $10 \mathrm{cc}$
2 $24 \mathrm{cc}$
3 $15 \mathrm{cc}$
4 $12 \mathrm{cc}$
Mechanical Properties of Solids

140999 A wire of length $L$ and cross-sectional area $A$ is made of a material with Young's modulus Y. If the wire is stretched by an amount $x$, the work done is

1 $\frac{\mathrm{YAx}^{2}}{2 \mathrm{~L}}$
2 $\frac{\mathrm{YAx}^{2}}{\mathrm{~L}}$
3 $\frac{Y A x}{2 L}$
4 $\mathrm{YAx}^{2} \mathrm{~L}$
Mechanical Properties of Solids

141000 A uniform cylindrical rod of length ' $L$ ' area of cross-section ' $A$ ' and Young's modulus ' $Y$ ' is acted upon by the forces as shown in the figure. The elongation of the rod is

1 $\frac{3 \mathrm{FL}}{5 \mathrm{AY}}$
2 $\frac{2 \mathrm{FL}}{5 \mathrm{AY}}$
3 $\frac{3 \mathrm{FL}}{8 \mathrm{AY}}$
4 $\frac{8 \mathrm{FL}}{3 \mathrm{AY}}$
Mechanical Properties of Solids

141001 A composite steel rod $P Q R$ is made of two rods $P Q$ and $Q R$ as shown in figure. The lengths of two rods $P Q$ and $Q R$ are $20 \mathrm{~cm}$ and $10 \mathrm{~cm}$ respectively. The area of cross-section of the longer rod is $2 \times 10^{-4} \mathrm{~m}^{2}$ and that of the shorter $\operatorname{rod}$ is $1 \times 10^{-4} \mathrm{~m}^{2}$. If the composite $\operatorname{rod}$ is stretched with a force of $50 \times 10^{3} \mathrm{~N}$, the total elongation produced is
(Young's modulus of steel $=20 \times 10^{10} \mathrm{Nm}^{-2}$ )

1 $5 \mathrm{~mm}$
2 $0.5 \mathrm{~mm}$
3 $25 \mathrm{~mm}$
4 $2.5 \mathrm{~mm}$
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Mechanical Properties of Solids

140998 The compressibility of water is $6 \times 10^{-10} \mathrm{~N}^{-1} \mathrm{~m}^{2}$. If one litre is subjected to a pressure of $4 \times 10^{7} \mathrm{~N}$ $\mathrm{m}^{-2}$, the decrease in its volume is

1 $10 \mathrm{cc}$
2 $24 \mathrm{cc}$
3 $15 \mathrm{cc}$
4 $12 \mathrm{cc}$
Mechanical Properties of Solids

140999 A wire of length $L$ and cross-sectional area $A$ is made of a material with Young's modulus Y. If the wire is stretched by an amount $x$, the work done is

1 $\frac{\mathrm{YAx}^{2}}{2 \mathrm{~L}}$
2 $\frac{\mathrm{YAx}^{2}}{\mathrm{~L}}$
3 $\frac{Y A x}{2 L}$
4 $\mathrm{YAx}^{2} \mathrm{~L}$
Mechanical Properties of Solids

141000 A uniform cylindrical rod of length ' $L$ ' area of cross-section ' $A$ ' and Young's modulus ' $Y$ ' is acted upon by the forces as shown in the figure. The elongation of the rod is

1 $\frac{3 \mathrm{FL}}{5 \mathrm{AY}}$
2 $\frac{2 \mathrm{FL}}{5 \mathrm{AY}}$
3 $\frac{3 \mathrm{FL}}{8 \mathrm{AY}}$
4 $\frac{8 \mathrm{FL}}{3 \mathrm{AY}}$
Mechanical Properties of Solids

141001 A composite steel rod $P Q R$ is made of two rods $P Q$ and $Q R$ as shown in figure. The lengths of two rods $P Q$ and $Q R$ are $20 \mathrm{~cm}$ and $10 \mathrm{~cm}$ respectively. The area of cross-section of the longer rod is $2 \times 10^{-4} \mathrm{~m}^{2}$ and that of the shorter $\operatorname{rod}$ is $1 \times 10^{-4} \mathrm{~m}^{2}$. If the composite $\operatorname{rod}$ is stretched with a force of $50 \times 10^{3} \mathrm{~N}$, the total elongation produced is
(Young's modulus of steel $=20 \times 10^{10} \mathrm{Nm}^{-2}$ )

1 $5 \mathrm{~mm}$
2 $0.5 \mathrm{~mm}$
3 $25 \mathrm{~mm}$
4 $2.5 \mathrm{~mm}$