Four identical spheres, each of radius 10 ,cm | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(C) The given situation is shown in the figure where $A, B, C, D$ are the centers of the four spheres forming a square of side $a = 20 \,cm$.Since all

Vedclass · Accepted Answer

$10 \sqrt{2} \,cm$

Vedclass · Answer

(C) The given situation is shown in the figure where $A, B, C, D$ are the centers of the four spheres forming a square of side $a = 20 \,cm$.Since all four spheres are identical and have equal masses, the center of mass of the system will coincide with the geometric center of the square formed by their centers, denoted by point $O$.The distance of the center of mass from the center of any sphere (e.g., center $A$) is the distance $AO$.In a square of side $a = 20 \,cm$, the length of the diagonal $AC$ is given by $AC = \sqrt{a^2 + a^2} = a\sqrt{2} = 20\sqrt{2} \,cm$.The distance from the center of the square to any vertex is half the length of the diagonal:$AO = \frac{AC}{2} = \frac{20\sqrt{2}}{2} = 10\sqrt{2} \,cm$.

Four identical spheres, each of radius $10 \,cm$ and equal mass $1 \,kg$, are placed on a horizontal surface touching each other such that their centers are located at the vertices of a square of side $20 \,cm$. What is the distance of their center of mass from the center of any sphere?

Similar Questions

Three identical spheres each of diameter $2\sqrt{3} \text{ m}$ are kept on a horizontal surface such that each sphere touches the other two spheres. If one of the spheres is removed,then the shift in the position of the centre of mass of the system is

Two particles of masses $2$ g and $4$ g are situated at the opposite ends, $A$ and $B$ of a wooden bar respectively. Let $l(AB) = 9$ cm. The center of mass of the system will be

Three identical spheres of radius $r$ are placed on a horizontal surface such that they touch each other. These spheres are arranged such that their centers form an equilateral triangle. The center of mass of this system will be at ........

When two masses $m$ and $M$ $(M > m)$ are connected,where will the center of mass be located?

$A$ slender uniform rod of length $L$ is balanced vertically at a point $P$ on a horizontal surface having some friction. If the top of the rod is displaced slightly to the right,the position of its centre of mass at the time when the rod becomes horizontal is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module