Two blocks of mass m and 2 m are slowly just placed in contact with each other on a rough fixed inclined plane as shown. Initially, both blocks are at rest on the inclined plane. The coefficients of f

Question

Two blocks of mass m and 2 m are slowly just placed in contact with each other on a rough fixed inclined plane as shown. Initially, both blocks are at rest on the inclined plane. The coefficients of friction between the blocks and the inclined surface are shown. There is no friction between the blocks. Column I gives four situations. Column II gives conditions under which statements in Column I are true. Match the statement in Column I with the corresponding conditions in Column II. Column I Column II The magnitude of acceleration of both blocks are the same, if μ 1 = μ 2 > tan θ The normal reaction between both the blocks is zero, if μ 1 > μ 2 > tan θ The net reaction exerted by the inclined surface on each block makes the same angle with the inclined surface, if μ 1 < μ 2 < tan θ The net reaction exerted by the inclined surface on the block of mass 2 m is double that of the net reaction exerted by the inclined surface on the block of mass m , if μ 1 = μ 2 < tan θ μ 1 < tan θ ; μ 2 > tan θ

TestHub · Accepted Answer

If tan θ > μ 1 , m will slide & If tan θ > μ 2 , 2 m will slide & If tan θ < μ 1 , m will not slide tan θ < μ 2 , 2 m will not slide. [(A)] When magnitude of acceleration of both blocks are same acceleration of m : a 1 = g sin θ − μ 1 g cos θ acceleration of m : a 2 = g sin θ − μ 2 g cos θ will start {After sliding will start Thus, acceleration of both blocks will be same either when μ 1 = μ 2 or when both the blocks are at rest (a = 0 ) when μ 1 > μ 2 > tan θ , both blocks are at rest ( a = 0 ) Thus for (A), P, Q & S are matching (A) → P, Q, S, [(B)] Normal reaction between both the blocks will be zero, either when a 1 = a 2 (both blocks are moving together) or when a 1 > a 2 Σ100 a 1 = a 2 [ P , Q , S ] Now if a 1 > a 2 ⇒ μ 2 > μ 1 [ R , T ] [B] → [P,Q,R,S,T]

	Column I		Column II
	The magnitude of acceleration of both blocks are the same, if		$μ_{1} = μ_{2} > tan θ$
	The normal reaction between both the blocks is zero, if		$μ_{1} > μ_{2} > tan θ$
	The net reaction exerted by the inclined surface on each block makes the same angle with the inclined surface, if		$μ_{1} < μ_{2} < tan θ$
	The net reaction exerted by the inclined surface on the block of mass $2 m$ is double that of the net reaction exerted by the inclined surface on the block of mass $m$ , if		$μ_{1} = μ_{2} < tan θ$
			$μ_{1} < tan θ$ ; $μ_{2} > tan θ$

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