A 4-kilogram object revolves in a circle at constant speed with a centripetal force of 200 N. If the mass is doubled while speed and radius stay the same, what is the new centripetal force?

A 4-kilogram object revolves in a circle at constant speed with a centripetal force of 200 N. If the mass is doubled while speed and radius stay the same, what is the new centripetal force?

• A. 800 N
• B. 50 N
• C. 400 N
• D. 100 N

Answer: (C)

Centripetal force depends linearly on mass when speed and radius are fixed. The formula is F_c = m v^2 / r, so the factor that changes when you change the mass is m, while v^2/r stays the same. If you double the mass from 4 kg to 8 kg, the centripetal force also doubles: F_c becomes 2 × 200 N = 400 N.

Centripetal force depends linearly on mass when speed and radius are fixed. The formula is F_c = m v^2 / r, so the factor that changes when you change the mass is m, while v^2/r stays the same. If you double the mass from 4 kg to 8 kg, the centripetal force also doubles: F_c becomes 2 × 200 N = 400 N.