એક ટેબલ પર એક-એક રૂપિયાના દસ સિક્કાઓ ઉપરાઉપરી મૂકેલ છે. દરેક સિક્કાનું દળ m છે. નીચેના કિસ્સાઓમાં બળનાં માન અને દિશા જણાવો :

$(a)$ નીચેથી ગણતાં $7$ મા સિક્કા પર તેનાથી ઉપરના બધા સિક્કાઓ વડે લાગતું બળ

$(b)$ આઠમા સિક્કા વડે $7$ મા સિક્કા પર લાગતું બળ

$(c)$ છઠ્ઠા સિક્કાનું $7$ મા સિક્કા પરનું પ્રતિક્રિયાબળ

$(a)$ Force on the seventh coin is exerted by the weight of the three coins on its top.

Weight of one coin $=m g$

Weight of three coins $=3\, mg$

Hence, the force exerted on the $7^{\text {th }}$ coin by the three coins on its top is $3$ $mg$. This force acts vertically downward.

$(b)$ Force on the seventh coin by the eighth coin is because of the weight of the eighth coin and the other two coins (ninth and tenth) on its top.

Weight of the eighth coin $=m g$

Weight of the ninth coin $=m g$

Weight of the tenth coin $=m g$

Total weight of these three coins $=3\, m g$

Hence, the force exerted on the $7^{\text {th }}$ coin by the eighth coin is $3$ $mg$. This force acts vertically downward.

$(c)$ The $6^{\text {th }}$ coin experiences a downward force because of the weight of the four coins $\left( {{7^{th}}} \right){\rm{ }}$.

$8^{\text {th }}, 9^{\text {th }},$ and $10^{\text {th }}$ on its top.

Therefore, the total downward force experienced by the $6^{\text {th }}$ coin is $4 \,m g$.

As per Newton's third law of motion, the $6^{\text {th }}$ coin will produce an equal reaction force on

the $7^{\text {th }}$ coin, but in the opposite direction. Hence, the reaction force of the $6^{\text {th }}$ coin on the $7^{\text {th }}$ coin is of magnitude $4 \,mg$. This force acts in the upward direction.