First slide

Connected bodies

Question

A chain has mass m and contains n identical links, where n is an odd integer. The chain is hanging vertically from the roof. If g is the acceleration due to gravity, the force exerted by the middle link on the one that is below it is

Moderate

A

$\frac{(n + 1) m g}{2 n}$
B

$\frac{(n - 1) m g}{n}$
C

$\frac{(n + 1) m g}{n}$
D

$\frac{(n - 1) m g}{2 n}$

Solution

. $\frac{(n + 1)}{2} w i l l b e t h e m i d d l e o n e (\frac{n - 1}{2}) w i l l b e b e l o w t h e m i d d l e w e i g h t o f e a c h l i n k i s \frac{m g}{n} w e i g h t o f \frac{n - 1}{2} l i n k w i l l b e t h e f o r c e g i v e n b y t h e m i d d l e o n e n e x t t o i t a n d w i l l g e t t h e s a m e r e a c t i o n f o r c e$

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