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JEE Main 2005 (AIEEE) · Composite & Cut-Out Bodies

Composite & Cut-Out Bodies question from JEE Main 2005 (AIEEE)

Q14JEE Main 2005 · AIEEEDifficult

Composite & Cut-Out Bodies

A T shaped object with dimensions shown in the figure, is lying on a smooth floor. A force ′F⃗′'\vec{F}' is applied at the point PP parallel to AB,AB, such that the object has only the translational motion without rotation. Find the location of PP with respect to C.C.

Figure

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Answer: (d)

  1. For pure translation, F⃗\vec{F} must pass through the centre of mass.
  2. Same rod material: AB has mass mm (length LL), stem has mass 2m2m (length 2L2L).
  3. Measured up from C: stem centre at LL, AB at 2L2L.
  4. ycm=2m(L)+m(2L)3m=4L3y_{cm} = \frac{2m(L) + m(2L)}{3m} = \frac{4L}{3}
  5. So the answer is (d) 43L\frac{4}{3}L above C.
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