Mechanical Properties of Solids and Fluids

A particle of unit mass is moving along the x-axis under the influence of a force and its total energy is conserved. Four possible forms of the potential energy of the particle are given in column I (

*a*and*U*_{0}are constants). Match the potential energies in column I to the corresponding statement(s) in column II.Column I |
Column II |
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(A) | ${U}_{1}\left(x\right)=\frac{{U}_{0}}{2}{\left[1-{\left(\frac{x}{a}\right)}^{2}\right]}^{2}$ | (P) | The force acting on the particle is zero at x = a. |

(B) | ${U}_{2}\left(x\right)=\frac{{U}_{0}}{2}{\left(\frac{x}{a}\right)}^{2}$ | (Q) | The force acting on the particle is zero at x = 0. |

(C) | ${U}_{3}\left(x\right)=\frac{{U}_{0}}{2}{\left(\frac{x}{a}\right)}^{2}\mathrm{exp}\left[-{\left(\frac{x}{a}\right)}^{2}\right]$ | (R) | The force acting on the particle is zero at x = −a |

(D) | ${U}_{4}\left(x\right)=\frac{{U}_{0}}{2}\left[\frac{x}{a}-\frac{1}{3}{\left(\frac{x}{a}\right)}^{3}\right]$ | (S) | The particle experiences an attractive force towards x = 0 in the region |x| < a. |

(T) | The particle with total energy $\frac{{U}_{0}}{4}$ can oscillation about the point x = −a. |

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JEE Advanced 2015

Young's modulus, Y = $\frac{\mathrm{longitudinal}\mathrm{stress}}{\mathrm{longitudinal}\mathrm{strain}}$

Bulk modulus,

Modulus of rigidity, G = $\frac{\mathrm{tangential}\mathrm{stress}}{\mathrm{tangential}\mathrm{strain}}$

Volume (V) = (area of cross-section) × height

In column I, the quantities are mentioned and in column II the factor on which the given quantities may depend are mentioned.

Match the following

Bulk modulus,

*β*= $\frac{\mathrm{volume}\mathrm{stress}}{\mathrm{volume}\mathrm{strain}}$Modulus of rigidity, G = $\frac{\mathrm{tangential}\mathrm{stress}}{\mathrm{tangential}\mathrm{strain}}$

Volume (V) = (area of cross-section) × height

In column I, the quantities are mentioned and in column II the factor on which the given quantities may depend are mentioned.

Match the following

Column I |
Column II |
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P. | Y | 1. | Length |

Q. | β |
2. | Nature of material |

R. | G | 3. | Area of cross-section |

S. | V | 4. | temperature |

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JEE Advanced 0