LIST - I | LIST - II | ||
---|---|---|---|

P. | $$\overrightarrow r $$(t)=$$\alpha $$ $$t\,\widehat i + \beta t\widehat j$$ | 1. | $$\overrightarrow p $$ |

Q. | $$\overrightarrow r \left( t \right) = \alpha \cos \,\omega t\,\widehat i + \beta \sin \omega t\,\widehat j$$ | 2. | $$\overrightarrow L $$ |

R. | $$\overrightarrow r \left( t \right) = \alpha \left( {\cos \omega t\,\widehat i + \sin \omega t\widehat j} \right)$$ | 3. | K |

S. | $$\overrightarrow r \left( t \right) = \alpha t\,\widehat i + {\beta \over 2}{t^2}\widehat j$$ | 4. | U |

5. | E |

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:

A small block of mass 1 kg is released from rest at the top of a rough track. The track is circular arc of radius 40 m. The block slides along the track without toppling and a frictional force acts on it in the direction opposite to the instantaneous velocity. The work done in overcoming the friction up to the point Q, as shown in the figure, below, is 150 J. (Take the acceleration due to gravity, g = 10 m/s^{2})

The speed of the block when it reaches the point Q is