A meter scale is held vertically with one of the ends on the floor. Its other end falls to floor without scale slipping. the velocity of the upper end of the scale when it hits the floor is?? 9.8m/s 8.9 45 5.4

1 Answer
A08
May 29, 2018

When the meter scale is held vertically with one end on the floor, its center of mass is at a height of #=0.5\ m#. Let #M# be its mass.

GPE#=Mxx9.81xx0.5=4.905M\ J# ........(1)

Let #v# be the velocity of the top end as it hits the floor. According to Law of conservation of energy

#"Loss of GPE"\ =\ "Rotational KE"#
#=>4.905M=1/2Iomega^2# .......(2)
where #I# is its moment of inertia of scale about its end and #omega# is angular velocity of falling end.

Now #I=1/3ML^2=1/3M(1)^2=M/3#
and #omega=v/r=v/1=v#. Inserting these values in (2) we get

#4.905M=1/2xxM/3xxv^2#
#=>v^2=sqrt(4.905xx2xx3)#
#=>v=5.42\ ms^-1#

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