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(B) Let the radius of each sphere be $r$. Since the spheres are identical and touching,the distance between the centres of adjacent spheres is $2r$.Le

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$\frac{KL + KM}{3}$

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(B) Let the radius of each sphere be $r$. Since the spheres are identical and touching,the distance between the centres of adjacent spheres is $2r$.Let the positions of the centres be $x_K = 0$,$x_L = 2r$,and $x_M = 4r$.The mass of each sphere is $m = 1 \ kg$.The centre of mass $X_{cm}$ is given by $X_{cm} = \frac{m x_K + m x_L + m x_M}{m + m + m} = \frac{0 + 2r + 4r}{3} = \frac{6r}{3} = 2r$.Since $KL = 2r$ and $KM = 4r$,we have $X_{cm} = KL = \frac{KM}{2}$.Alternatively,$X_{cm} = \frac{KL + KM}{3} = \frac{2r + 4r}{3} = 2r$.Thus,the distance of the centre of mass from $K$ is $\frac{KL + KM}{3}$.

Three identical spheres,each of mass $1 \ kg$,are placed touching each other with their centres on a straight line. Their centres are marked $K, L$,and $M$ respectively. The distance of the centre of mass of the system from $K$ is

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