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The bulk modulus of a spherical object is B. If it is subjected to uniform pressure p, the fractional decrease in radius is

(a)$\frac{P}{B}$

(b) $\frac{B}{3p}$

(c) $\frac{3p}{B}$

(d)$\frac{p}{3B}$

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The Young's modulus of steel is twice that of brass. Two wires of same length and of same area of cross-section, one of steel and another of brass are suspended from the same roof. If we want the lower ends of the wires to be at the same level, then the weight added to the steel and brass wires must be in the ratio of

(a)1:2

(b)2:1

(c)4:1

(d)1:1

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The Young's modulus of a wire of length L and radius r is $YN/{m}^{2}.$ If the length and radius are reduced to L/2 and r/2, then its Young's modulus will be -

(a) 1:1 (b) 1:4

(c) 1:8 (d) 8:1

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A force *F* is needed to break a copper wire having radius *R*. The force needed to break a copper wire of radius 2*R* will be

(a) *F*/2 (b) 2*F*

(c) 4*F *(d) *F*/4

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The relationship between Young's modulus *Y*, Bulk modulus K and modulus of rigidity n is

(a) $Y=\frac{9nK}{n+3K}$ (b) $\frac{9YK}{Y+3K}$

(c) $Y=\frac{9nK}{3+K}$ (d) $Y=\frac{3nK}{9n+K}$

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If *x* longitudinal strain is produced in a wire of Young's modulus *y*, then energy stored in the material of the wire per unit volume is-

(a) $y{x}^{2}$ (b) $2y{x}^{2}$

(c) $\frac{1}{2}{y}^{2}x$ (d) $\frac{1}{2}y{x}^{2}$

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The Young's modulus of a rubber string 8 *cm* long and density $1.5kg/{m}^{3}$ is $5\times {10}^{8}N/{m}^{2}$, is suspended on the ceiling in a room. The increase in length due to its own weight will be

(a) $9.6\times {10}^{-5}m$ (b) $9.6\times {10}^{-11}m$

(c) $9.6\times {10}^{-3}m$ (d) 9.6 m

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*A* and *B* are two wires of same material. The radius of *A* is twice that of *B*. They are stretched by the same load. Then the stress on *B* is

(a) Equal to that on *A * (b) Four times that on *A*

(c) Two times that on *A * (d) Half that on *A*

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