Pulling Cloth from Beneath Dishes and Action Reaction
STATEMENT-1
A cloth covers a table. Some dishes are kept on it. The cloth can be pulled out without dislodging the dishes from the table.
because
STATEMENT-2
For every action there is an equal and opposite reaction.
Options
Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1
Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1
Statement-1 is True, Statement-2 is False
Statement-1 is False, Statement-2 is True
Topics & Concepts
Step-by-Step Solution
To determine the correct option, let us analyze both statements:
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Analysis of Statement-1:
When a tablecloth is pulled horizontally with a very large acceleration, the time duration during which it remains in contact with the dishes is extremely small.The maximum horizontal force that can be exerted by the cloth on a dish of mass is limited by kinetic friction:
where is the coefficient of kinetic friction and is the acceleration due to gravity.The impulse delivered to the dish during this brief time interval is:
The velocity acquired by the dish is therefore:
The displacement of the dish during this interaction is approximately:
As the cloth is jerked out quickly, , which causes and . Due to the dishes' inertia of rest (governed by Newton's First Law of Motion), they remain virtually unaffected and stay in place without being dislodged from the table.
Hence, Statement-1 is True.
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Analysis of Statement-2:
"For every action there is an equal and opposite reaction."
This is a statement of Newton's Third Law of Motion, which is a fundamental and universally true law of Newtonian mechanics.Hence, Statement-2 is True.
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Relationship between the Statements:
While both statements are physically true, the phenomenon described in Statement-1 is primarily explained by the inertia of the dishes (Newton's First Law) and the concept of impulse over a very short duration, not by Newton's Third Law (action-reaction pairs).Therefore, Statement-2 is NOT the correct explanation for Statement-1.
Thus, the correct choice is B.