Question

(a)
A body tied to one end of a string is made to revolve in a vertical
circle. Derive an expression for the velocity of the body and tension in
the string at any point.​

Answer 1

Answer :

An expression for the velocity of the body and tension in

the string at any point.​

T = m/r ($u^{2}$ -3gh + gr)  

Explanation :

Let v represent the body's velocity at point P on the vertical circle. Let's assume that L represents the lowest position. The velocity is "u" at L.

By using the Conservation of energy, we have:

The energy at point P is equal to the energy at point L.

$\frac{1}{2} mv^{2} + mgh = } \frac{1}{2} mu^{2}$

$v^{2}$+ 2gh = $u^{2}$

Let's think about the centripetal force at point P:

$T =\frac{mv^{2} }{r}- mgcos\alpha$  ---- Equation (1) (1)

Equation (1) is solved by substituting the values, and the result is:

T=m/r($u^{2}$ -3gh + gr)

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