Question

plz dove this que its argent very argent​

Answer 1

Given :

Mass of L-shaped lamina = 6kg

To Find :

Position of centre of mass.

Solution :

❖ Centre of mass is an Imaginary point where the whole mass of system can be assumed to be concentrated.

Let's divide the lamina into three equal parts as shown in the attached image.

Mass of each part will be 6/3 = 2 kg

♦ Centre of mass of each part :

1) R₁ = (a/4 , 3a/4)

2) R₂ = (a/4 , a/4)

3) R₃ = (3a/4 , a/4)

♦ Position of COM of lamina :

$\sf:\implies\:R_{COM}=\dfrac{M_1R_1+M_2R_2+M_3R_3}{M_1+M_2+M_3}$

• M₁ = M₂ = M₃ = 2 kg

$\sf:\implies\:R_{COM}=\dfrac{2(R_1+R_2+R_3)}{3(2)}$

$\sf:\implies\:R_{COM}=\dfrac{R_1+R_2+R_3}{3}$

$\sf:\implies\:R_{COM}=\dfrac{\left(\dfrac{a}{4},\dfrac{3a}{4}\right)+\left(\dfrac{a}{4},\dfrac{a}{4}\right)+\left(\dfrac{3a}{4},\dfrac{a}{4}\right)}{3}$

$\sf:\implies\:R_{COM}=\left[\left(\dfrac{a+a+3a}{4\times3}\right),\left(\dfrac{3a+a+a}{4\times3}\right)\right]$

$:\implies\:\underline{\boxed{\bf{\gray{R_{COM}=\left(\dfrac{5a}{12},\dfrac{5a}{12}\right)}}}}$