A uniform thin wooden plank AB of length L and mass M is kept on a table with its B end slightly outside the edge of the table. When an impulse J is given to the end B , the plank moves up with centre of mass rising a distance 'h' from the

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A uniform thin wooden plank AB of length L and mass M is kept on a table with its B end slightly outside the edge of the table. When an impulse J is given to the end B , the plank moves up with centre of mass rising a distance 'h' from the surface of the table. Then-

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Correct answer: C. J ² / 2 M ² ~g < h < 9 ~J ² / 8 M ² ~g

Case-I Considering angular momentum w.r.t. end A = Angular velocity just after impulse then ( ) ( ML ² 3 )= J ( L ) = 3 ~J ML velocity of CM V _ cm ₁ = L 2 = 3 ~J 2 M ......(1) Case-II Apply conservation o moment, if V _ cm ₂ = Velocity of CM just after impulse then M V _ cm ₂ = J V _ cm ₂ = J M ......(2) comparing (1) & (2) V _ cm ₂ 1 2 M ( J M )² h _ > J ² 2 M ² ~g ......(4) Use (3) & (4) Hence J ² 2 M ² ~g < h _ < 9 ~J ² 8 M ² ~g

A uniform thin wooden plank AB of length L and mass M is kept on a table with its B end slightly outside the edge of the table. When an impulse J is given to the end B , the plank moves up with centre of mass rising a distance 'h' from the surface of the table. Then-

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