IIT-JEE 2007 · Paper 1 · Physics Q10

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PhysicsAssertion and reason+3 / -1Question 10 of 66

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.

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

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

Statement-1 is True, Statement-2 is False

Statement-1 is False, Statement-2 is True

Answer and worked solution

Official answer: C

Statement 1. On the level surface all the kinetic energy $\frac12mv^2$ is lost to friction. On the incline the block stops after $d=\dfrac{v^2}{2g(\sin30°+\mu\cos30°)}$ , and the loss is the friction work
$\mu mg\cos30°\,d=\frac{\mu\cos30°}{\sin30°+\mu\cos30°}\cdot\frac12mv^2<\frac12mv^2.$
True.

Statement 2. The coefficient of friction is a property of the surfaces; it does not depend on the inclination. False.

(C)

Topics:Friction Work-energy theorem

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IIT-JEE 2007 · Paper 1, Physics question 10