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salantis [7]
3 years ago
7

A 20-cm-long, 190 g rod is pivoted at one end. A 19 g ball of clay is stuck on the other end.

Physics
1 answer:
MaRussiya [10]3 years ago
8 0

Answer:

0.76 s

Explanation:

We are given that

Length of rod,L=20 cm=\frac{20}{100}=0.20m

1 m=100 cm

Mass of rod,M=190 g=\frac{190}{1000}=0.19kg

Mass of ball,m=19 g=\frac{19}{1000}=0.019 kg

Using 1 kg=1000g

We have to find the period if the rod and clay swing as a  pendulum.

Moment of inertia of rod-clay=Moment of inertia of rod+moment of inertia of clay

I_{rod-clay}=I_{rod}+I_{clay}

I_{rod-clay}=\frac{1}{3}ML^2+mL^2

Substitute the values then we get

I_[rod-clay}=\frac{1}{3}(0.19)(0.20)^2+(0.019)(0.20)^2

I_{rod-clay}=3.29\times 10^{-3} kgm^2

Now, the center of mass of the combination of the rod and clay is given by

y=\frac{Md_1+md_2}{M+m}

Substitute d_1=\frac{L}{2}=Distance between pivot and the center of the rod

d_2=L=The distance  between rod and clay

Using the formula

y=\frac{0.19\times \frac{0.20}{2}+0.019\times 0.20}{0.19+0.019}

y=0.1091 m

Time period of the oscillation of the system of the rod and the clay is given by

T=2\pi\sqrt{\frac{I_{rod-clay}}{(M+m)yg}}

g=9.8m/s^2

Using the formula

Time period=2\times 3.14\sqrt{\frac{3.29\times 10^{-3}}{(0.19+0.019)\times 9.8\times 0.1091}}

Time-period=0.76 s

Hence, the period =0.76 s

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