Question

Four solid spheres each of mass M and radius R are placed with their centres on the four comers of a rectangle. If b is a breadth of rectangle and its length is twice of its breadth, then find moment of inertia of the system about an axis along one of the breadth of the rectangle.

Options

• `8/5  "MR"^2 + 4  "Mb"^2`

• `8/5  "MR"^2 + 8  "Mb"^2`

• `8/5  "MR"^2 + 2  "Mb"^2`

• `8/5  "MR"^2 + 10  "Mb"^2`

Answer 1

`8/5  "MR"^2 + 8  "Mb"^2`

Explanation:

`"M.l. of 1 about AB" = 2/5 "MR"^2`

`"M.I of 4 about AB" = 2/5 "MR"^2`

`"M.I. of 2 about AB" = 2/5 "MR"^2 + "M"(2"b")^2`

`= 2/5  "MR"^2 + 4  "Mb"^2`

`"M.I. of 3 about AB" = 2/5  "MR"^2 + 4  "Mb"^2`

`"I"_("AB") = 8/5  "MR"^2 + 8  "Mb"^2`