Question

A small stone of mass m ( = 200 g ) is held underwater in a tall jar and allowed to fall as shown in the following figure. The free-body diagram of the stone is also shown.

(i) What does F₂ represent?

(ii) What does m₁ represent?

(iii) What is the net force acting on the stone?

(iv) What is the acceleration of the stone as it falls through water? Neglect the force due to viscosity. Assume that volume of stone = 80 cml, density of water = 1.0 g cm^-3 and acceleration due to gravity g = 10 ms^-2.

Answer 1

(i) F₂ represents the buoyant force acting on the stone in an upward direction.

(ii) m₁ represents the apparent mass of the stone during motion through the water.

(iii) Net force acting on the stone = F₁ - F₂ = (m - m₁)g.

(iv) Mass of stone = 200 gm = 0.2 kg.
Volume of stone = 80 cm³ = 80 x 10^-6 m³.
Density of water = 1 gcm^-3 = 1000 kgm³.
Acceleration due to gravity = 10 ms^-2.

Upthrust = V x p x g.

Upthrust = 80 x 10^-6 x 1000 x 10 = 0.8 N.

Weight of the stone = mass x gravity = 0.2 x 10 = 2 N. Resultant weight of the stone = weight - upthrust = 2 N - 0.8 N = 1.2 N

Resultant acceleration of the qravity = m x a' m x a' = 1.2 N
a'= 1. 2/0.2 = 6ms^-2.

Resultant acceleration of the stone as it falls through the water is 6 ms^-2,