Answer:
Explanation:
Given
mass of object [tex]m=7 kg[/tex]
kinetic Energy [tex]k=36\ J[/tex]
Tension in string [tex]T=326\ N[/tex]
mass is moving in a horizontal circle so tension is providing the centripetal acceleration
therefore [tex]T=\frac{mv^2}{r}----1[/tex]
where r=radius of circle
kinetic energy of particle [tex]k=\frac{1}{2}mv^2----2[/tex]
divide 1 and 2 we get
[tex]\frac{T}{k}=\frac{\frac{mv^2}{r}}{\frac{1}{2}mv^2}[/tex]
[tex]\frac{T}{k}=\frac{2}{r}[/tex]
[tex]r=\frac{2k}{T}=\frac{2\times 36}{326}[/tex]
[tex]r=0.2208\ m[/tex]
The radius of the circle is 0.221 m
The radius of the circular path is determined from the following formula,
K.E = ¹/₂mv²
T = mv²/r
Where;
[tex]\frac{T}{K.E} = \frac{mv^2}{0.5rmv^2} \\\\0.5Tr = K.E\\\\r = \frac{K.E}{0.5T} \\\\r = \frac{36}{0.5 \times 326} \\\\r = 0.221 \ m[/tex]
Thus, the radius of the circle is 0.221 m.
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