Question

One end of rod of length L and mass M1 is rivetted to the centre of a uniform circular disc of radius r and mass M2 so that both are coplanar. The centre of mass of the combination from the centre of the disc is

Answer 1

Given that,

Length of rod = L

Mass of rod = M₁

Mass of disc = M₂

We need to calculate the centre of mass of the combination from the centre of the disc

Using formula of center of mass

$r_{com}=\dfrac{m_{1}x_{1}+m_{2}x_{2}}{m_{1}+m_{2}}$

Put the value into the formula

$r_{com}=\dfrac{M_{1}\times\dfrac{L}{2}+M_{2}\times0}{M_{1}+M_{2}}$

$r_{com}=\dfrac{M_{1}L}{2(M_{1}+M_{2})}$

Hence, The centre of mass of the combination from the centre of the disc is $\dfrac{M_{1}L}{2(M_{1}+M_{2})}$

Answer 2

Given that,

Length of rod = L

Mass of rod = M₁

Mass of disc = M₂

We need to calculate the centre of mass of the combination from the centre of the disc

Using formula of center of mass

$r_{com}=\dfrac{m_{1}x_{1}+m_{2}x_{2}}{m_{1}+m_{2}}$

Put the value into the formula

$r_{com}=\dfrac{M_{1}\times\dfrac{L}{2}+M_{2}\times0}{M_{1}+M_{2}}$

$r_{com}=\dfrac{M_{1}L}{2(M_{1}+M_{2})}$

Hence, The centre of mass of the combination from the centre of the disc is $\dfrac{M_{1}L}{2(M_{1}+M_{2})}$

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