# Question #e5ff1

Apr 7, 2016

At the bottom

#### Explanation:

For the body to continue with circular motion, a centripetal force is required. If we assume the body moves at the same speed, then the centripetal force will be constant ${F}_{c} = m {v}^{2} / r$

If we define T as the tension and mg as the object's weight

At the bottom:
${T}_{b} - m g = {F}_{c}$ .
Tension always acts towards the centre. The tension net of the weight has to provide the centripetal force. This can rearranged as:

${T}_{b} = {F}_{c} + m g$

At the top:
${T}_{t} + m g = {F}_{c}$. The tension and the weight provide centripetal force, which is the same as:

${T}_{t} = {F}_{c} - m g$

And at middle:
${T}_{m} = {F}_{c}$ (weight acts perpendicular to tension and centripetal force, so affects neither)

Hence if ${F}_{c}$ is constant, then the tension is greatest at the bottom.