Question

A metal cylinder measures 3.0 cm in diameter, is 12.0 cm high, and has a mass of 750 g. The cylinder hangs from a string attached to a scale that measures weight in Newtons (N). The cylinder is lowered into a cylindrical beaker of water until it is submerged completely. The diameter of the beaker is 10.0 cm. (a) By how much does the height of the water in the beaker rise when the cylinder is submerged? (b) What weight does the scale read after the cylinder is submerged?

Answer 1

Answer with Explanation:

We are given that

Diameter of cylinder,$d_1=$3 cm

Radius,$r_1=\frac{d_1}{2}=\frac{3}{2}=1.5cm=1.5\times 10^{-2} m$

1m=100 cm

Height,h=12 cm=$\frac{12}{100}=0.12 m$

Mass,m=750 g=$\frac{750}{1000}=0.75kg$

1kg=1000 g

Diameter of beaker,$d_2=10 cm$

Radius of beaker,$r_2=\frac{d_2}{2}=\frac{10}{2}=5cm$

A.$\pi r^2_2h_2=\pi r^2_1 h_1$

$h_2=\frac{r^2_1}{r^2_2}h$

$h_2=\frac{(1.5)^2}{(5)^2}\times 12=1.08 cm$

Hence, the height of the water in the beaker rises when the cylinder is submerged=1.08 cm

B.Weight read on the scale after the cylinder is submerged

$w=mg-\rho A_1h_1g$

Where $g=9.8 m/s^2$

$A_1=\pi r^2_1$

Density of water=$\rho=1000kg/m^3$

$w=0.75\times 9.8-1000\times \pi(1.5\times 10^{-2})^2\times 0.12\times 9.8$

$w=6.52 N$