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A string is wrapped on a wheel of moment...

A string is wrapped on a wheel of moment of inertia 0.20 kg-m^2 and radius 10 cm and goes through a light pulley to support a block of mas 2.0 kg as shown in figure. Find the acceleration of the block.

Text Solution

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The correct Answer is:
B
`I=0.20kg-m^2` (bigger pulley)
`r=10cm=0.1m, Smaller pulley is light
`Mass of the block m=2kg`
Therefore `mg-T=ma`……….1
`Txxr=Ixxalpha`
`rarr T=(Ia)/r^2`………….2
`rarr mg=(m+I/r^2)a` [Using 2 and 1]
`rarr a=(mg)/((m+I/r^2))`
`=(2xx9.8)/{(2+(0.2/0.01)}`
`=19.6/22=0.89m/s^2`
therefore acceleration of the block
`=0.89m/s^2`
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