KVPY SX SB Exam 19-Nov-2017 Question Paper

Question : 93 of 120

Marks: +1, -0

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-

$h > 9J^2 \/8M^2 g$
$h = J^2 \/2M^2 g$
$J^2 \/2M^2 g < h < 9J^2 \/8M^2 g$
$h < J^2 \/2M^2 g$

Validate

Solution:

Case-IConsidering angular momentum w.r.t. end A
ω = Angular velocity just after impulse then

(ω)({ML^2}/3)=J(L)

ω={3J}/{ML}

⇒ velocity of CM

V_{cm_1} ={ωL}/2={3J}/{ML}

...(1)
Case-II
Apply conservation o moment, if 2

V_{cm_2}

= Velocity of CM just after impulse
then

MV_{cm_2}=J

V_{cm_2}=J/M

...(2)
comparing (1) & (2)
$V_{cm_2}⇒ velocity of CM just after impulse would be between above two extreme values
with (1),

Mgh_\max. < 1/2(M)({3J}/{2M})^2

⇒

h_\max < {9J^2}/{8M^2g}

...(3)

Mgh_\max. < 1/2(M)({ J}/{ M})^2

h_\max < { J^2}/{2M^2g}

...(4)
Use (3) & (4)
Hence

{ J^2}/{2M^2g} < h_\max <{9 J^2}/{8M^2g}

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