$Assertion$ : $A$ man and a block rest on a smooth horizontal surface. The man holds a rope which is connected to the block. The man cannot move on the horizontal surface.
$Reason$ : $A$ man standing at rest on a smooth horizontal surface cannot start walking due to the absence of friction (The man is only in contact with the floor as shown).

  • A
    If both Assertion and Reason are correct and the Reason is a correct explanation of the Assertion.
  • B
    If both Assertion and Reason are correct but Reason is not a correct explanation of the Assertion.
  • C
    If the Assertion is correct but Reason is incorrect.
  • D
    If both the Assertion and Reason are incorrect.

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Consider a system of blocks $A$, $B$, and $X$ as shown in the figure. The blocks $A$ and $B$ have equal mass $m$ and are connected by a massless string through a massless pulley. The coefficient of friction between block $A$ and $X$, and between block $B$ and $X$, is $\mu = 0.5$. If block $X$ moves on the horizontal frictionless surface, what should be its minimum acceleration $a$ such that blocks $A$ and $B$ remain stationary relative to $X$? ($g =$ acceleration due to gravity.)

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