Question

A small object of mass m, at the end of a light cord, is held horizontally at a distance r from a fixed support as
shown. The object is then released. What is the tension in the cord when the object is at the lowest point of its
swing?
(1)m
(2) mg
(3) 2mg
(4) 3mg​

Answer 1

Answer:

Option (4) 3mg

Explanation:

The object will undergo a circular motion

Any object undergoing a circular motion experiences a centripetal force

the potential energy of the object at height r will be mgr

At the lowest point the whole potential energy will have converted in kinetic energy

Therefore,

$\frac{1}{2}mv^2=mgr$

$\imlies \frac{v^2}{r}=2g$

Now at the lowest point if the tension is T then centripetal force will be acting outwards i.e. vertically downwards and the weight is also vertically downwards. these two forces will be balanced by the Tension

Therefore,

$T=mg+m\frac{v^2}{r}$

$\implies T=mg+m\times 2g$

$\implies T=3mg$

Therefore, the tension in the cord is 3mg

Hope this helps.

Answer 2

Answer:

Option (4) 3mg

Explanation:

The object will undergo a circular motion

Any object undergoing a circular motion experiences a centripetal force

the potential energy of the object at height r will be mgr

At the lowest point the whole potential energy will have converted in kinetic energy

Therefore,

Now at the lowest point if the tension is T then centripetal force will be acting outwards i.e. vertically downwards and the weight is also vertically downwards. these two forces will be balanced by the Tension

Therefore,

Therefore, the tension in the cord is 3mg

Step-by-step explanation: