Q5.26 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 - (mv_1^2))/R           mg - T_2 + (mv_1^2))/R

    (d)    mg - T_1 - (mv_1^2))/R          mg + T_2 + (mv_1^2))/R

T_1 and v_1 denote the tension and speed at the lowest point. T_2 and v_2 denote corresponding values at the highest point.

Answers (1)

The FBD of stone at the lowest point is shown below :

                                        Laws of motion,   20275

Using Newton's law of motion, 

                                                      T\ -\ mg\ =\ \frac{mv^2}{r}

The FBD of stone at the highest point is given below :

                                                      Laws of motion,   20275 (2)

Using Newton's law of motion we have :

                                                           T\ +\ mg\ =\ \frac{mv^2}{r}

Thus option (a) is correct.

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