You are given three radioactive samples (α, β, and γ) and can only dispose of one. the other two you must keep, one in your hand, the other in your pocket. how would you minimize your exposure risk?

Keep alpha in hand, keep beta in pocket, dispose of gamma radioactive sample

Explanation:

Alpha particles:

Alpha particles are the particles which cannot penetrate most of the matter. The outer layer of the skin or a piece of paper may be sufficient to stop the alpha particles.

The Radioactive material that emits the alpha particles  can be harmful when they are swallowed, inhaled, or absorbed into blood stream through wounds.

Thus, α radioactive sample can be kept in hand.

Beta particles:

Beta particles are the particles which can be stopped by a few mm of a substance like aluminum layer or by clothing.

Beta particles can penetrate the skin and can cause radiation damage, such as skin burns.

Thus, β radioactive sample can be kept in pocket.

Gamma rays:

Gamma rays are the rays which are penetrating. Many feet of concreted layers or some inches of metal lead are needed to stop them.

Gamma rays are the radiation hazard for the entire human body.

They attack the DNA and can cause lethal defects.

Thus, γ radioactive sample is to be disposed off.

fgravity=10x10=100n case 1

fgravity=30x20=600n case 2

6 times more