First slide

Location of centre on mass for multiple point masses

Question

A T-shaped object with dimensions as shown in the figure, is lying on a smooth floor. A force 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.

Moderate

A

$\frac{4}{3} l$
B

l
C

$\frac{2}{3} l$
D

$\frac{3}{2} l$

Solution

Here, the force F must be acting on CM of system.
Let, $m_{1} = m, m_{2} = 2 m$
Taking D as origin, $y_{CM} = \frac{m \times 0 + 2 m l}{m + 2 m} = \frac{2 l}{3}$
From C, $C P = 2 l - \frac{2 l}{3} = \frac{4 l}{3}$

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