Question

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 eighth coin.

(c) The reaction of the $6^{th}$ coin on the $7^{th}$ coin.

Answer 1

(a) Force on the seventh coin is exerted by the weight of the three coins on its top.Weight of one coin = mg
Weight of three coins = 3mg
Hence, the force exerted on the 7th coin by the three coins on its top is 3mg. This force acts vertically downward.

(b) Force on the seventh coin by the eight coin is same as the Force on the 7th coin due to top three coins.

(c) The 6th coin experiences a downward force because of the weight of the four coins (7th, 8th, 9th, and 10th) on its top.
Therefore, the total downward force experienced by the 6th coin is 4mg.
As per Newtons third law of motion, the 6th coin will produce an equal reaction force on the 7th coin, but in the opposite direction. Hence, the reaction force of the 6th coin on the 7th coin is of magnitude 4mg. This force acts in the upward direction.