Question

A thin uniform rectangular plate (lamina) is of mass m and dimensions 2a by a. Choose a coordinate system OXYZ such that the plate lies in the XY plane.

a) ( x = a, y = 2a )
b) ( x = 2a, y = a )
c) ( x = a, y = a )
d) ( x = 2a, y = 2a )

Answer 1

A coordinate system OXYZ such that the plate lies in the XY plane is ( x = a, y = a ).

Therefore, correct option is c) ( x = a, y = a )

Step-by-step explanation:

For a thin uniform rectangular plate with dimensions 2a by a, the appropriate coordinate system is (x = a, y = a).

Choosing the coordinate system (x = a, y = a) aligns with the center of mass of the rectangular plate. This choice simplifies calculations related to the plate's mass distribution and facilitates analyses involving moments of inertia and other mechanical properties.

When dealing with uniform objects, aligning the coordinate system with the center of mass often simplifies mathematical expressions, making it more convenient for solving problems in mechanics and dynamics.

Therefore, correct option is c) ( x = a, y = a )