Ten one-rupee coins are put on top of each other on a table. Each coin has a mass m . Give the magnitude and direction of
(a) the force on the `7^(th)` coin (counted from the bottom due to all the coins on its top .
(b) the force on the `7^(th)` coin by the eigth coin.
(c ) the reaction of the `6^(th)` coin one th `7^(th)` coin .

Explanation

(a) The force on 7 th coin is due to weight of the three coins lying above it Therefore
` F = (3 m ) kg f = (3 mg ) N `
where g is acceleration due to gravity . This force acts vertically downwards .
(b) The eighth coin is alredy under the weight of two coins above it and it has its own weight too . Hence force on 7 th coin due to 8 th coin is sum of the two forces i . e
` F = 2 m + m = (3 m ) kg f = (3 mg ) N `
The force acts vertically downwards .
(c) The sixth coin is under the weight of four coins above it
Reaction ` R = - F = - 4 m (kg f ) = - (4 mg ) N `
Minus sigh indicates that the reaction acts vertically upwards opposite to the weight .