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A ball filled with air has a mass of 1.5 kg and its volume is 0.01 m3

. Calculate the force needed to hold it below the water surface (g ≈ 10 m.s

−2

).

A50 N
B850 N
C100 N
D115 N

Verified Answer :

MathPhys

Answer:

e) none of the previous options

Explanation:

Draw a free body diagram of the ball. There are three forces:

  • Weight force mg pulling down, where m is mass and g is gravity
  • Buoyancy force ρVg pushing up, where ρ is the density of water, V is the displaced volume, and g is gravity
  • Applied force F pushing down

The ball is not moving, so according to Newton's second law of motion, the sum of the forces is zero.

∑F = ma

ρVg − mg − F = 0

F = ρVg − mg

F = g (ρV − m)

Plugging in values:

F = (10 m/s²) ((1000 kg/m³) (0.01 m³) − 1.5 kg)

F = 85 N

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