Q77 / 90 · JEE Main 2019 (08 Apr Shift 2) · Physics

A uniform rectangular thin sheet $A B C D$ of mass $M$ has length $a$ and breadth $b$ , as shown in the figure. If the shaded portion $H B G O$ is cut-off, the coordinates of the centre of mass of the remaining portion will be:

Correct answer
A
$\frac{5 a}{12}, \frac{5 b}{12}$
B
$\frac{5 a}{3}, \frac{5 b}{3}$
C
$\frac{2 a}{3}, \frac{2 b}{3}$
D
$\frac{3 a}{4}, \frac{3 b}{4}$

Solution

If the total mass of object mass $M$ then the mass removed part will be $\frac{M}{4}$ .

$X_{C M} = \frac{M \cdot \frac{a}{2} - \frac{M}{4} (\frac{3 a}{4})}{M - \frac{M}{4}} = \frac{\frac{M a}{2} - \frac{3 M a}{16}}{\frac{3 M}{4}} = \frac{5}{12} a$
$Y_{C M} = \frac{M \cdot \frac{b}{2} - \frac{M}{4} (\frac{3 b}{4})}{M - \frac{M}{4}} = \frac{\frac{M b}{2} - \frac{3 M b}{16}}{\frac{3 M}{4}} = \frac{5}{12} b$

Hence, the correct answer is option: 'A'.

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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:

Solution

Relevant Questions

A uniform rectangular thin sheet $A B C D$ of mass $M$ has length $a$ and breadth $b$ , as shown in the figure. If the shaded portion $H B G O$ is cut-off, the coordinates of the centre of mass of the remaining portion will be: