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Two identical spheres of mass M are fastened to opposite ends of a rod of length 2 L. The radii of the spheres are negligible when compared to the length 2L, and the rod has negligible mass. This system is initially at rest with the rod horizontal and is free to rotate about a frictionless axis through the center of the rod. The axis is horizontal and perpendicular to the plane of the page. A bug of mass 3M lands gently on the sphere on the left. Assume that the size of the bug is small compared with the length of the rod.

After the bug lands, the rod begins to rotate. What correctly describes the change in the magnitude of the angular momentum of the bug-rod-spheres system and the change in gravitational potential energy of the bug-rod-spheres-Earth system as the rod rotates but before the rod becomes vertical?

Answer :

Answer:

Angular Momentum increase

Gravitational Potential Energy decrease

Explanation:

given data

mass = 3M

length = 2L

solution

when rod is rotate till it become vertical

so torque is counter clockwise

and there therefore angular speed goes on increase and there angular moment also increase

but as that gravitational potential energy will be decrease

Onyebuchinnajigo

The angular momentum of the system will increase, while the potential energy of the system will decrease after the bug lands.

The given parameters;

  • mass of the two identical spheres, = M
  • length of the rods, = 2L
  • mass of the bug, = 3M

The change in the angular momentum is calculated as;

[tex]\Delta L = \Delta I\omega[/tex]

After the bug lands, the total mass of the system increases and the angular speed increases from zero. Consequently, the angular momentum of the system will increase.

The change in potential energy is calculated as;

[tex]\Delta P.E = mg(\Delta h)[/tex]

After the bug lands, the height of the system decreases to zero, which leads to a decrease in the potential energy of the system.

Thus, we can conclude that the angular momentum of the system will increase, while the potential energy of the system will decrease after the bug lands.

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