Question

A girl is holding a ball with a diameter of 4.10 cm and average density of 0.0841 g/cm3 under water. Determine the force (in N) needed to hold it completely submerged.

Answer 1

The force needed to hold the ball completely submerged is 0.323N

Step-by-step explanation:

In this question we have given,

diameter of ball= 4.1 cm

Therefore, radius of ball,
`r=(4.1)/(2) cm`

`r=(4.1)/(2* 100) m`

`r=.0205 m`

density of ball,
`\rho_(b)=0.0841 gcm^(-3)`

`\rho_(b)=84.1 kgm^(-3)`

density of water,
`\rho_(w)=1000kgm^(-3)`

we know that, volume of sphere is given by following formula,

`V=(4\pi* r^3)/(3)`

we know that,

`density=(mass)/(volume)\\ mass=density * volume`

Therefore,

`mass* gravity =density * volume * gravity`

or

`Force =density * volume * gravity`..............(1)

Here,

`density= \rho_(w)-\rho_(b)`

Put values of density, volume and gravity in equation (1)

`Force =(\rho_(w)-\rho_(b)) * (4\pi* (4.1)/(2))/(3)* 9.8`.

`Force =(1000-84.1}) *(4 \pi * (.0205)^3 * 9.8)/(3)`

Force=0.323N

the force needed to hold the ball completely submerged is 0.323N