Figure shows a block P of mass m resting on a horizontal smooth floor at a distance ℓ from a rigid wall. Block is pushed toward right by a distance 3 ℓ /2 and released. When block passes from its mean

Question

Figure shows a block P of mass m resting on a horizontal smooth floor at a distance $ℓ$ from a rigid wall. Block is pushed toward right by a distance $3 ℓ /2$ and released. When block passes from its mean position another block of mass $m_{1}$ is placed on it which sticks to it due to friction. Find the value of $m_{1}$ so that the combined block just avoids collision with the left wall.

TestHub · Accepted Answer

Energy: 2 1 ​ k ( 2 3 ℓ ​ ) 2 = 2 1 ​ m v 2 ⇒ v = 2 3 ℓ ​ m k ​ ​ . Sticking at mean position: v ′ = m + m 1 ​ m v ​ . Just avoiding the wall needs amplitude ℓ : A ′ = k ( m + m 1 ​ ) ​ m v ​ = 2 3 ℓ ​ m + m 1 ​ m ​ ​ = ℓ . 4 9 ​ m + m 1 ​ m ​ = 1 ⇒ m 1 ​ = 4 5 m ​ . Option (B).

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JEE Main 2027 (Class 12+)