JEE Challenger
More from Laws of Motion

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

A

Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1

B

Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1

Correct
C

Statement-1 is True, Statement-2 is False

D

Statement-1 is False, Statement-2 is True

Step-by-Step Solution

To determine the correct option, let us analyze both statements:

  1. Analysis of Statement-1:
    When a tablecloth is pulled horizontally with a very large acceleration, the time duration Δt\Delta t 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 mm is limited by kinetic friction:
    fk=μkN=μkmgf_k = \mu_k N = \mu_k mg
    where μk\mu_k is the coefficient of kinetic friction and gg is the acceleration due to gravity.

    The impulse delivered to the dish during this brief time interval Δt\Delta t is:
    J=∫0Δtfk dt=μkmgΔtJ = \int_0^{\Delta t} f_k \, dt = \mu_k mg \Delta t

    The velocity acquired by the dish is therefore:
    v=Jm=μkgΔtv = \frac{J}{m} = \mu_k g \Delta t

    The displacement of the dish during this interaction is approximately:
    Δx≈12μkg(Δt)2\Delta x \approx \frac{1}{2} \mu_k g (\Delta t)^2

    As the cloth is jerked out quickly, Δt→0\Delta t \to 0, which causes Δx→0\Delta x \to 0 and v→0v \to 0. 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.

  2. 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.

  3. 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.