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Two masses M and m are attached to a ver...

Two masses M and m are attached to a vertical axis by weightless threads of combined length l . They are set in rotational motion in a horizontal plane about this axis with constant angular velocity `omega` . If the tensions in the threads are the same during motion, the distance of M from the axis is

A

`((M+m)/(m))l`

B

`((M+m)/(M))l`

C

`((M)/(M_m))l`

D

`((M)/(M+m))l`

Text Solution

Verified by Experts

The correct Answer is:
D

Suppose that M is at a distance x from the axis of rotation, so that the distance of m from the axis
`=l-x`
They are moving with the same angular velocity `omega.`
`therefore" The tensions in the threads will be"`
`T_(1)=Mxomega^(2) and T_(2)=m(l-x)omega^(2)" "thereforeMx=ml=mx`
`therefore x(M+m)=ml" "therefore x=(ml)/(M+m)`
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