Question

An inverted T-shaped object is placed on a smooth horizontal floor as shown in figure
A force $F$ is applied on the system as shown in figure. The value of $x$ so that the system performs pure transional motion is

• A. $\frac{L}{4}$
• B. $\frac{3L}{4}$
• C. $\frac{L}{2}$
• D. $\frac{2L}{2}$

Answer 1

The correct option is A $\frac{L}{4}$

If the force is applied to the center of mass of the whole system then the system will perform only transitional motion not rotational motion .

For COM:

$X_{COM}=\frac{x_1{m}_1+x_2{m}_2}{m_1+m_2}$

$x_{COM}=\frac{0.M+M\times \frac{L}{2}}{M+M}$

$X_{COM}=\frac{L}{4}$