A small stone of mass m(=200g) is held under water in a jar and is allowed to fall as shown in fig. the forces acting on stone are also shown.

(i) What does `F_(2)` represent ?
(ii) What does `m_(1)` represent?
(iii) What is the net force acting on stone?
(iv) What is the acceleration of stone as it falls through water? Neglect the force due to viscosity. Assume that the volume of stone
`=80cm^(3)`, density of water `=1.0gcm^(-3)` and acceleration due to gravity `g=10ms^(-2)`

Explanation

(i) `F_(2)` represents the upthrust on stone due to water.
(ii) `m_(1)` represents the mass of water displaced by stone
(iii) Net force acting on stone `=F_(1)-F_(2)` (downwards)
(iv) Given `V=80cm^(3),rho=1 g cm^(-3), g=10ms^(-2)`,
`m=200g=200/1000kg=0.2kg`
`:.` weight of stone `F_(1)=mg=0.2kgxx10ms^(-2)=2N`
Mass of water displaced `m_(1)=v rho =80xx1=80g`
`=80/1000kg=0.08kg`
upthrust `F_(2)=m_(1)g=0.08kgxx10ms^(-2)=0.8N`
Hence net downward force on stone
`=F_(1)-F_(2)`
`=2-0.8=1.2N`
`:.` Acceleration`=("Force")/("Mass")=(1.2N)/(0.2kg)=6m^(-2)`