STATEMENT–1: A block of mass starts moving on a rough horizontal surface with a velocity . It stops due to friction between the block and the surface after moving through a certain distance.

Question

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.

STATEMENT–2: The coefficient of friction between the block and the surface decreases with the increase in the angle of inclination. [2007]

Smart Achievers · Accepted Answer

(3)

In the first case the mechanical energy is completely converted into heat because of friction, i.e., decrease in mechanical energy $= \frac{1}{2} m v^{2}$

While in second case, a part of mechanical energy is converted into heat due to friction but another part of mechanical energy is retained in the form of potential energy of the block, i.e., Decrease in mechanical energy $= \frac{1}{2} m v^{2} - m g h$

Therefore statement 1 is correct.

Statement 2 is wrong. The coefficient of friction between the block and the surface does not depend on the angle of inclination.

Solution

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

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

3 Statement–1 is True, Statement–2 is False

4 Statement–1 is False, Statement–2 is True

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