First slide

Centre of mass(com)

Question

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 :

Easy

A

(1.25m, 1.50m)
B

(0.75m, 0.75m)
C

(0.75m, 1.75m)
D

(1m, 1.75m)

Solution

$\begin{array}{l} C o o r d i n a t e s o f t w o s h a d e d p a r t s (h a v i n g e q u a l a r e a a n d m a s s) a r e (0.5, 1) a n d (1, 2.5) \\ I n v e c t o r f o r m, \\ {\vec{r}}_{c m} = \frac{m_{1} \hat{r_{1}} + m_{2} \hat{r_{2}}}{m_{1} + m_{2}} \\ \Rightarrow {\vec{r}}_{c m} = \frac{2 \times (\frac{\overset{\land}{i}}{2} + \overset{\land}{j}) + 2 \times (\overset{\land}{i} + \frac{5 \overset{\land}{j}}{2})}{4} \\ \Rightarrow {\vec{r}}_{c m} = \frac{3}{4} \overset{\land}{i} + \frac{7}{4} \overset{\land}{j} \\ H e n c e c o o r d i n a t e s o f C O M i s (0.75, 1.75) \end{array}$

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