Question

a chain of mass M and length L is held vertical by fixing its upper end to a rigid support .the tension in the chain at a distance y from the rigid support is :

Answer 1

Mass per length = M/L

Mass of length L - y = M/L * (L - y) ∵ The point supports the lower side weight of string

Hence the weight is M( 1 - y/L ) g.

The answer would be T = M( 1 - y/L) g

Answer 2

Given that,

Mass of chain = M

Length of chain = L

Distance = y

We know that,

Mass per unit length =$\dfrac{M}{L}$

Mass of length (L-y)=$\dfrac{M}{L}\times(L-y)$

The lower side of the weight of the chain

We need to calculate the weight

Using formula of weight

$W=mg$

Put the value of m

$W=\dfrac{M}{L}\times(L-y)\times g$

We need to calculate the tension in the chain at a distance y from the rigid support

Using formula of tension

Tension of the string = weight of the string

$T=W$

$T=\dfrac{M}{L}\times(L-y)\times g$

$T=\dfrac{M}{L}\times L(1-\dfrac{L}{y})g$

$T=(1-\dfrac{L}{y})Mg$

Hence, The tension in the chain at a distance y from the rigid support is $(1-\dfrac{L}{y})Mg$