Work, Energy and Power

*K*is the kinetic energy,

*U*is the potential energy and

*E*is the total energy. Match each path in List-I with those quantities in List-II, which are

**conserved for that path.**

LIST–I |
LIST–II |
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P. |
$\overrightarrow{r}$(t) = αt$\hat{i}$ + βt$\hat{j}$ |
1. |
$\overrightarrow{p}$ |

Q. |
$\overrightarrow{r}$(t) = α cos ωt$\hat{i}$ + β sin ωt$\hat{j}$ |
2. |
$\overrightarrow{L}$ |

R. |
$\overrightarrow{r}$(t) = α (cos ωt$\hat{i}$ + sin ωt$\hat{j}$) |
3. |
K |

S. |
$\overrightarrow{r}\left(t\right)=at\hat{i}+\frac{\beta}{2}{t}^{2}\hat{j}$ | 4. |
U |

5. |
E |

Column II shows five systems in which two objects are labeled as X and Y, Also in each case a point P is shown. Column I give some statements about X and/or Y. Match these statements to the appropriate system(s) from column II.

Column I |
Column II |
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(A) | The force exerted by X on Y has a magnitude Mg | (p) |
Block Y of mass M left on a fixed inclined plane X, slides on it with a constant velocity |

(B) | The gravitational potential energy of X is continuously increasing | (q) |
Two ring magnets Y and Z each of mass M, are kept in frictionless vertical plastic stand so that they repeal each other. Y rests on the base X and Z hangs in air in equilibrium. P is the topmost point of the stand on the common axis of the two rings. The whole system is in a lift that is going up with a constant velocity |

(C) | Mechanical energy of the system X + Y is continuously decreasing | (r) |
A pulley Y of mass m |

(D) | The torque of the weight of Y about point P is zero | (s) |
A sphere Y of mass M is put in a nonviscous liquid X kept in a container at rest. The sphere is released and it moves down in the liquid |

(t) |
A sphere Y of mass M is falling with its terminal velocity in a viscous liquid X kept in a container |