Question

Two steel spheres of radius 2 cm and 5 cm are made to touch each other. The distance of their centre of mass from their point of contact is

Answer 1

Answer:

6.58 cm

Explanation:

We are given that two steel spheres of radius 2 cm and 5 cm.

We have to find the distance of their center of mass from their point of contact.

Let $\rho$ be the density of steel spheres.

Volume of sphere=$\frac{4}{3}\pi r^3$

Let origin is the center of mass of big sphere

CM=$\frac{m_1x_1+m_2x_2}{m_1+m_2}$

Substitute the values $x_1=0,x_2=5+2=7$ then we get

$CM=\frac{\frac{4}{3}\pi (2)^3\times \rho\times 0+\frac{4}{3}\pi (5)^3\rho\times 7 }{\frac{4}{3}\pi(2)^3\rho+\frac{4}{3}\pi (5)^3\rho}$

$CM=\frac{3500}{532}$

$CM=6.58 cm$

Hence, the distance of their center of mass from their point of contact is 6.58 cm in the bigger sphere from its center.