Which Japanese emperor played a significant role in the Meiji Restoration?

A body crosses the topmost point of a vertical circle with critical speed. What will be its centripetal acceleration when the string is horizontal?

A bucket tied at the end of $11.6 \mathrm{m}$ long string is whirled in a vertical circle with a constant speed. The minimum speed at which water from the bucket does not spill when it is at the highest position is:

A stone of mass $m$ tied to the end of a string revolves in a vertical circle of radius $R$. The net forces at the lowest and highest points of the circle directed vertically downwards are: [Choose the correct alternative]

        Lowest Point                                                        Highest Point
(a)    $mg-T_1$                                                           $mg+T_2$

(b)    $mg+T_1$                                                           $mg–T_2$

(c)    $mg+T_1-\frac{m{v_{\mathit{1}}}^2}{R}$                                              $mg-T_2+\frac{m{v_2}^2}{R}$

(d)    $mg-T_1+\frac{m{v_1}^2}{R}$                                             $mg+T_2+\frac{m{v_2}^2}{R}$

$T_1$ and $v_1$ denote the tension and speed at the lowest point. $T_1$ and $v_2$ denote corresponding values at the highest point.

Given in Figure are examples of some potential energy functions in one dimension. The total energy of the particle is indicated by a cross on the ordinate axis. In each case, specify the regions, if any, in which the particle cannot be found for the given energy. Also, indicate the minimum total energy the particle must have in each case. Think of simple physical contexts for which these potential energy shapes are relevant.

When a simple pendulum is rotated in a vertical plane with constant angular velocity, centripetal force is: