Question 175: Centre of Mass and Rotational Motion

Question

A uniform rectangular thin sheet ABCD of
mass M has length a and breadth b, as shown
in the figure. If the shaded portion HBGO is
cut-off, the coordinates of the centre of mass
of the remaining portion will be :-

Accepted Answer

X- coordinate of CM of remaining sheet
$${X_{cm}} = {{MX - mx} \over {M - m}}$$
= $${{\left( {4m} ight) 	imes \left( {{a \over 2}} ight) - M\left( {{{3a} \over 4}} ight)} \over {4m - m}} = {{5a} \over {12}}$$
Similarly y
cm
= $${{5b} \over {12}}$$
$$ 	herefore $$ $$CM\left( {{{5a} \over {12}},{{5b} \over {12}}} ight)$$

Answer

$$\left( {{{5a} \over 3},{{5b} \over 3}} \right)$$

Answer

$$\left( {{{2a} \over 3},{{2b} \over 3}} \right)$$

Answer

$$\left( {{{5a} \over 12},{{5b} \over 12}} \right)$$

Answer

$$\left( {{{3a} \over 4},{{3b} \over 4}} \right)$$

Centre of Mass and Rotational Motion

A uniform rectangular thin sheet ABCD of mass M has length a and breadth b, as shown in the figure. If the shaded portion HBGO is cut-off, the coordinates of the centre of mass of the remaining portion will be :-

Choose the correct answer: