Question

Assertion :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 ${30}^0$ 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. Reason: 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.
• D. Statement -1 is False, Statement-2 is True.

Answer 1

The correct option is C Statement -1 is True, Statement-2 is False.

$ME=KE+PE$

Decrease in KE in both cases is $\frac{m{v}^2}{2}$

In the first case, there is no change in PE.

In second case, as the block climbs up, it gains PE.

Hence, decrease in ME in second case is less.

Coefficient of friction is a material prpoerty of the surface and is thus independent of angle of inclination.

Hence, statement-1 is true and statement-2 is false.