# A ‘ ’ shaped object with dimensions shown in the figure, is lying on a smooth floor. A force ‘ ’ is applied at the point  parallel to , such that the object has only the translational motion without rotation. Find the location of  with respect to a) b) c) d)

## Question ID - 53248 :- A ‘ ’ shaped object with dimensions shown in the figure, is lying on a smooth floor. A force ‘ ’ is applied at the point  parallel to , such that the object has only the translational motion without rotation. Find the location of  with respect to a) b) c) d)

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(a)

For translatory motion the force should be applied on the centre of the mass of the body. So we have to calculate the location of centre of mass of ‘ ’ shaped object.

Let mass of rod  is  so the mass of the rod  will be

Let  is the centre of mass of rod  and  is the centre of mass of rod . We can consider that whole mass of the rod is placed at their respective centre of mass  mass  is placed at  and mass  is placed at

Taking point ‘ ’ at the origin position vector of point  and  can be written as  and  and

Position vector of centre of mass of the system

Hence the distance of centre of mass from

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 If the external forces acting on a system have zero resultant, the center of mass a) May move but not accelerate b) May Accelerate c) Must not move d) None of the above