arthham

JEE Advanced 2007 · Laws of Motion

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. Statement-2 : For every action there is an equal and opposite reaction.

Answer: B. Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1

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Written solution

Step 1: Analyze the forces acting on a dish.

The vertical forces cancel each other out, leaving friction as the only horizontal force acting on the dish.

N=mgN = mg Fhorizontal=fF_{\text{horizontal}} = f

Step 2: Analyze the effect of pulling the cloth quickly.

When the cloth is pulled rapidly, the contact time Δt\Delta t is extremely short.

a=fma = \frac{f}{m} Δv=aΔt=fmΔt\Delta v = a \Delta t = \frac{f}{m} \Delta t x≈12a(Δt)2x \approx \frac{1}{2} a (\Delta t)^2

As Δt→0\Delta t \to 0, both the change in velocity Δv\Delta v and the displacement xx approach zero, meaning the dishes remain virtually undisturbed.

Step 3: Identify the physical law explaining Statement-1.

According to Newton's First Law of Motion, a body at rest remains at rest unless acted upon by a net external force.

This property is known as the inertia of rest, which explains why Statement-1 is true.

Step 4: Analyze Statement-2.

Newton's Third Law states that action and reaction forces are equal and opposite.

fcloth→dish=−fdish→clothf_{\text{cloth} \to \text{dish}} = -f_{\text{dish} \to \text{cloth}}

This statement is universally true, but since action and reaction forces act on different bodies, they do not determine the motion of the dish alone. Thus, Statement-2 is not the explanation for Statement-1.

Step 5: Determine the correct option.

Both statements are true, but Statement-2 is not the correct explanation of Statement-1.

Answer: Statement-1 is True, Statement-2 is True; Statement-2 is not a correct explanation for Statement-1.

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