Work, Energy and Power

In the List-I below, four different paths of a particle are given as functions of time. In these functions, α and β are positive constants of appropriate dimensions and α ≠ β. In each case, the force acting on the particle is either zero or conservative. In List-II, five physical quantities of the particle are mentioned: $\overrightarrow{p}$ is the linear momentum, $\overrightarrow{L}$ is the angular momentum about the origin,

*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 |

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JEE Advanced 2018

A point object is moved from point A to B. There are a number of forces acting on that point object . Some forces are conservative and some are non-conservative.

Match the list-I with list-II

Match the list-I with list-II

List-I |
List-II |
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(P) | change in kinetic energy of the point object | (1) | Depends on frame of reference |

(Q) | work done by conservative forces | (2) | Does not depend on the frame of reference |

(R) | work done by non-conservative forces | (3) | Depends on path between A and B |

(S) | time taken to travel from A to B. | (4) | Does not depend on path between A and B |

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JEE Mains 0