The time taken by an object to slide down 45$$^\circ$$ rough inclined plane is n times as it takes to slide down a perfectly smooth 45$$^\circ$$ incline plane. The coefficient of kinetic friction between the object and the incline plane is :

For the given figures, choose the correct options :

An object moves at a constant speed along a circular path in a horizontal plane with center at the origin. When the object is at $$x=+2~\mathrm{m}$$, its velocity is $$\mathrm{ - 4\widehat j}$$ m/s. The object's velocity (v) and acceleration (a) at $$x=-2~\mathrm{m}$$ will be

The time period of a satellite of earth is 24 hours. If the separation between the earth and the satellite is decreased to one fourth of the previous value, then its new time period will become.