JEE Advanced · 2007 · 08 Apr 2007 · Paper 1 · Laws of Motion

STATEMENT-1
A block of mass

m

starts moving on a rough horizontal surface with a velocity

v

. It stops due to friction between the block and the surface after moving through a certain distance. The surface is now tilted to an angle of 30° with the horizontal and the same block is made to go up on the surface with the same initial velocity

v

. The decrease in the mechanical energy in the second situation is smaller than that in the first situation.
because
STATEMENT-2
The coefficient of friction between the block and the surface decreases with the increase in the angle of inclination.

(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
(C)Statement-1 is True, Statement-2 is False✓ Correct
(D)Statement-1 is False, Statement-2 is True

Answer: (C)

Solution

Statement-1 Analysis: On a horizontal surface, the decrease in mechanical energy equals the work done by friction:

Δ E_{1} = μ m g s_{1}

, where

s_{1}

is the distance traveled.

On an inclined surface at 30°, the block also gains potential energy as it moves up. The total decrease in mechanical energy is

Δ E_{2} = μ m g cos (30°) s_{2} + m g s_{2} sin (30°)

. Since the block travels a shorter distance on the incline (due to the component of gravity opposing motion), and considering the energy balance,

Δ E_{2} < Δ E_{1}

. Statement-1 is True.

Statement-2 Analysis: The coefficient of friction

μ

is a property of the surfaces in contact and does not change with the angle of inclination. Statement-2 is False.

Therefore, the answer is (C).

JEE Advanced · 2007 · 08 Apr 2007 · Paper 1 · Single correct option

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JEE Advanced · 2007 · 08 Apr 2007 · Paper 1 · Laws of Motion

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