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A straight rod AB of mass M and length L...

A straight rod `AB` of mass `M` and length `L` is placed on a frictionless horizontal surface. A horizontal force having contstant magnitude `F` and fixed direction starts acting at the end `A`. The rod is initially perpendicular to the force. Find the initial acceleration of end `B`.

Text Solution

Verified by Experts

The correct Answer is:
`2F//M`
Rod will have translational + rotational motion about cm.

For translation motion `a_(cm) = (F)/(m)`
For rotational motion
`F (L)/(2) = I alpha rArr F (L)/(2) = (mL^(2))/(12) xx alpha`
`alpha = (6F)/(mL)`
`a_(B) =(L)/(2) alpha - a_(cm) rArr a_(B) = (3F)/(m) -(F)/(m) rArr a_(B) = (2F)/(m)`.
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