JEE Main · 2020 · 08 Jan 2020 · Shift 1 · Conservation of Momentum

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The coordinates of centre of mass of a uniform flag shaped lamina (thin flat plate) of mass 4 kg. (the coordinates of the same are shown in figure) are:

(A) $(0.75 m, 0.75 m)$
(B) $(0.75 m, 1.75 m)$ ✓ Correct
(C) $(1.25 m, 1.50 m)$
(D) $(1 m, 1.75 m)$

Answer: (B)

Solution

The flag-shaped plate splits into two rectangles of equal mass,

2

kg each. The lower rectangle (

1 m \times 2 m

) has its centre of mass at

(\frac{1}{2}, 1)

and the upper rectangle (

1 m \times 1 m

) at

(1, \frac{5}{2})

. Combining them,

r_{c m} = \frac{2 ( \frac{1}{2} i ^ + j ^ ) + 2 ( i ^ + \frac{5}{2} j ^ )}{4} = \frac{3}{4} \hat{i} + \frac{7}{4} \hat{j}

, so the centre of mass lies at

(0.75 m, 1.75 m)

JEE Main · 2020 · 08 Jan 2020 · Shift 1 · Single correct option

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