Question

There are five bodies with their centre of
mass lying on X-axis. Then their
combined centre of mass
(a) lies only y-axis
(b) lies on z-axis
(c) lies on x-axis
(d) may be anywhere​

Answer 1

Answer:

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Answer 2

Answer:

The combined center of mass (c) lies on the x-axis

Explanation:

It is given that five bodies have their center of masses lying on the X-axis.

Let the masses be m₁, m₂, m₃, m₄, and m₅ and their corresponding x-coordinates be x₁, x₂, x₃, x₄, and x₅.

The center of mass of a distribution of mass in space is the unique point where the weighted relative position of the distributed mass sums to zero.

The combined center of mass is given as

x = Σmₙxₙ/M, y = Σmₙyₙ/M, z = Σmₙzₙ/M, where M is the total mass of the system.

Since the bodies lie on the X-axis, the y and z coordinates will be equal to zero. Therefore,

x = Σmₙxₙ/M, y = 0, z = 0.

Hence, the combined center of mass for the given system of five bodies will lie on the X-axis.

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