# 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) 3537

(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 Next Question :
 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 