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Standard XII

Physics

Gravitational Potential Energy

Two spheres o...

Question

Two spheres of mass $M$ and $7 M$ are connected by a rod whose mass is negligible, and the distance between the centers of each sphere is $d$ . How far from the center of the $7 M$ sphere is the Center of Mass for this object?

d / 8

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d / 7

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d / 2

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6 d / 7

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7 d / 8

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Solution

The correct option is A $d / 8$
Point C represents the centre of mass of the system.
Given : $m_{1} = 7 M$ $m_{2} = M$
Using $x = \frac{m_{1} x_{1} + m_{2} x_{2}}{m_{1} + m_{2}}$

$∴$ $x = \frac{(7 M) \times 0 + M d}{7 M + M} = \frac{d}{8}$

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Two spheres of mass M and 7M are connected by a rod whose mass is negligible, and the distance between the centers of each sphere is d. How far from the center of the 7M sphere is the Center of Mass for this object?

The correct option is A d/8Point C represents the centre of mass of the system.Given : m1=7M m2=MUsing x=m1x1+m2x2m1+m2∴ x=(7M)×0+Md7M+M=d8

Two spheres of mass $M$ and $7 M$ are connected by a rod whose mass is negligible, and the distance between the centers of each sphere is $d$ . How far from the center of the $7 M$ sphere is the Center of Mass for this object?

The correct option is A $d / 8$
Point C represents the centre of mass of the system.
Given : $m_{1} = 7 M$ $m_{2} = M$
Using $x = \frac{m_{1} x_{1} + m_{2} x_{2}}{m_{1} + m_{2}}$

$∴$ $x = \frac{(7 M) \times 0 + M d}{7 M + M} = \frac{d}{8}$