Worat4 als 2. \( \mathrm{i} * \mathrm{in}=\mathrm{in} \). it \( 1 r=m, x+1 \) ha. the trot Uran an L. 1 itim in int. 4. IIm ria o Morit.
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$X_{1}+x_{2}=r$ $\ldots$..(i) and $m_{1} x_{1}=m_{2} x_{2}$ ...(ii) From Eqs. (i) and (ii), $x_{1}=\frac{m_{2} r}{m_{1}+m_{2}}$ and $x_{2}=\frac{m_{1} r}{m_{1}+m_{2}}$ $\therefore$ $I_{A B}=m_{1} x_{1}^{2}+m_{2} x_{2}^{2}=\frac{m_{1} m_{2} r^{2}}{m_{1}+m_{2}}$
Gravitation
Round 2
If $1_{1}=\int_{0}^{1} x^{m}(1-x)^{n} d x$ and $1_{2}=\int_{0}^{1} x^{n}(1-x)^{m} d x$, where $m$ and $n$ are $>0$, then (a) $\quad l_{1}=l_{2}$ (b) $1_{1}=\frac{\mathrm{m}}{\mathrm{n}} \mathrm{l}_{2}$ (c) $1_{1}=\frac{n}{m} l_{2}$ $\left(\right.$ d) $1_{1}=(m+n) l_{2}$
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