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  • A T shaped object with dimensions shown in the figure , is lying on a smooth floor. A force <img alt="\vec{F}" src="https://learn.careers360.com/latex-image/?%5Cdpi%7B100%7D%20%5Cvec%7BF%7

A T shaped object with dimensions shown in the figure , is lying on a smooth floor. A force \vec{F} is applied at the point P parallel to AB such that the object has only the translational motion without rotation. Find the location of  P with respect to C

Option: 1

\frac{4}{3}l


Option: 2

l


Option: 3

\frac{3}{4}l


Option: 4

\frac{3}{2}l


Answers (1)

best_answer

As we learnt in

Centre of Mass of a system of N discrete particles -

x_{cm}=\frac{m_{1}x_{1}+m_{2}x_{2}.........}{m_{1}+m_{2}.......}

y_{cm}=\frac{m_{1}y_{1}+m_{2}y_{2}+m_{3}y_{3}.........}{m_{1}+m_{2}+m_{3}.......}

z_{cm}=\frac{m_{1}z_{1}+m_{2}z_{2}+m_{3}z_{3}.........}{m_{1}+m_{2}+m_{3}.......}

- wherein

m1, m2 ........... are mass of each  particle  x1, x2 ..........y1, y2 ............ z1, z2 are respectively x, y, & z coordinates of particles.

 

 

It is a case of translation motion without rotation. The force should act at the centre of mass

Y_{cm}=\frac{(m\times 2l)+(2m\times l)}{m+2m}=\frac{4l}{3}

Posted by

SANGALDEEP SINGH

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