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A bowling ball (which we can regard as a uniform sphere) has a mass of 5.44 kg and a diameter of 0.216 m. A baseball has a mass of 0.145 kg. If you connect these two balls with a lightweight rod, what must be the distance between the center of the bowling ball and the center of the baseball so that the system of the two balls and the rod will balance at the point where the rod touches the surface of the bowling ball?

Respuesta :

lublana

Answer:

4.16 m

Explanation:

We are given that

[tex]m_1=5.44 kg[/tex]

[tex]d_1=0.216 m[/tex]

[tex]r_1=\frac{d_1}{2}=\frac{0.216}{2}=0.108 m[/tex]

[tex]m_2=0.145 kg[/tex]

We have to find the distance between centers of the bowling ball and the center of baseball.

Suppose, distance between centers of two balls=l

Radius of second ball=[tex]r_2=l-r_1=l-0.108[/tex]

For balance rod

[tex]T_{net}=0[/tex]

[tex]m_1gr_1-m_2gr_2=0[/tex]

[tex]5.44\times 0.108-0.145(l-0.108)=0[/tex]

[tex]5.44\times 0.108=0.145(l-0.108)[/tex]

[tex]l-0.108=\frac{5.44\times 0.108}{0.145}=4.052[/tex]

[tex]l=0.108+4.052=4.16 m[/tex]

Hence, the distance between the centers of two balls=4.16 m

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