First slide

Centre of mass(com)

Question

Three points particles of masses 1.0kg, 1.5kg and 2.5kg are placed at three corners of right angle triangle of sides 4.0cm, 3.0cm and 5.0cm as shown in the figure. The centre of mass of the system is at a point.

Easy

A

0.6cm right and 2.0cm above 1kg mass
B

0.9cm right and 2.0cm above 1kg mass
C

2.0cm right and 0.9cm above 1kg mass
D

1.5cm right and 1.2cm above 1kg mass

Solution

Take 1kg mass at origin
$\begin{array}{l} C o o r d i n a t e s o f 1 k g : (0, 0) \\ C o o r d i n a t e s o f 1.5 k g : (3, 0) \\ C o o r d i n a t e s o f 2.5 k g : (0, 4) \\ X_{c m} = \frac{\sum_{}^{} m x}{\sum_{}^{} m} \\ \Rightarrow X_{c m} = \frac{1 \times 0 + 1.5 \times 3 + 2.5 \times 0}{5} = 0.9 c m \\ a n d Y_{c m} = \frac{\sum_{}^{} m y}{\sum_{}^{} m} \\ Y_{c m} = \frac{1 \times 0 + 1.5 \times 0 + 2.5 \times 4}{5} = 2 c m \end{array}$

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