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

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?

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Maris 5 years 2021-07-20T19:12:46+00:00 1 Answers 22 views 0

Answers ( )

  1. Gerda
    0
    2021-07-20T19:14:42+00:00
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    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

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