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Question: Four particles each of mass m are placed at the corners of a square of side lenght l. The radius of ...

Four particles each of mass m are placed at the corners of a square of side lenght l. The radius of gyration of the system about an axis perpendicular to the square and passing through its centre is:

A

1/21 / \sqrt { 2 }

B

1/2

C

l

D
Answer

1/21 / \sqrt { 2 }

Explanation

Solution

Moment of inertia of system about point P.

=4m(l2)2= 4 m \left( \frac { l } { \sqrt { 2 } } \right) ^ { 2 } =2ml2= 2 m l ^ { 2 }

and 4mK2 = 2ml2

∴ K=l2K = \frac { l } { \sqrt { 2 } }