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 $^{\circ}$ 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.

Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

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Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion

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Assertion is correct but Reason is incorrect

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Both Assertion and Reason are incorrect

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Solution

The correct option is C Assertion is correct but Reason is incorrect
Decrease in mechanical energy in first case
$= E_{i} - E_{f} = \frac{1}{2} m v^{2} - 0 = \frac{1}{2} m v^{2}$
Decrease in mechanical energy in second case
$= E_{i} - E_{f} = \frac{1}{2} m v^{2} - m g h$
Further, $μ$ does not depend in angle of inclination

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Statement I: 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 a certain distance. The surface is now tilted to an angle of $30^{\circ}$ 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 II: The coefficient of friction between the block and the surface decreases with the increase in the angle of inclination.

Assertion: A proton and an $α$ - particle are projected with the same kinetic energy at right angle to a uniform magnetic field, then the $α$ - particle will move along a circular path of smaller radius than the proton.

Reason : $B q v = \frac{m v^{2}}{r}$ holds good for the charged particle moving in a circular path in a uniform magnetic field.

Choose the most appropriate correct option:

Assertion (A) Bond angle in ethers is slightly less than the tetrahedral angle.
Reason (R) There is a repulsion between the two bulky (- R) groups.
(a) Assertion and reason both are correct and reason is correct explanation of assertion.
(b) Assertion and reason both are wrong statements.
(c) Assertion is correct statement but reason is wrong statement.
(d) Assertion is wrong statement but reason is correct statement.
(e) Both assertion and reason are correct statements but reason is not correct explanation of assertion.

Q. Assertion: A body is moving along a straight line such that its velocity varies with time as shown in figure. Magnitude of displacement of the body from

t = 0

t = 12

s is the same as the distance travelled by it in the given time duration.

Reason: For unidirectional motion of a body, |displacement|=distance.

ASSERTION: n-Pentane and n-Hexane belong to a homologous series.

REASON: n-Pentane and n-Hexane belong to the same class of hydrocarbons and they differ by a - $C H_{2}$ - group.

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The correct option is C Assertion is correct but Reason is incorrectDecrease in mechanical energy in first case =Ei−Ef=12mv2−0=12mv2Decrease in mechanical energy in second case =Ei−Ef=12mv2−mghFurther, μ does not depend in angle of inclination