Search any question & find its solution
Question:
Answered & Verified by Expert
Two bodies of masses $m_{1}$ and $m_{2}$ are separated by a distance $R$. The distance of the centre of mass of the bodies from the mass $m_{1}$ is
Options:
Solution:
2778 Upvotes
Verified Answer
The correct answer is:
$\frac{m_{2} R}{m_{1}+m_{2}}$
The bodies are separated by a distance $R$. so the coordinates of $m_{1}$ and $m_{2}$ will be (0,0) and $(R, 0)$
From the formula of centre of mass,
$$
\begin{aligned}
X_{\mathrm{cm}} &=\frac{m_{1} x_{1}+m_{2} x_{2}}{m_{1}+m_{2}} \\
&=\frac{m_{1} \times 0+m_{2} \times R}{m_{1}+m_{2}} \\
X_{\mathrm{cm}} &=\frac{m_{2} \cdot R}{m_{1}+m_{2}}
\end{aligned}
$$
From the formula of centre of mass,
$$
\begin{aligned}
X_{\mathrm{cm}} &=\frac{m_{1} x_{1}+m_{2} x_{2}}{m_{1}+m_{2}} \\
&=\frac{m_{1} \times 0+m_{2} \times R}{m_{1}+m_{2}} \\
X_{\mathrm{cm}} &=\frac{m_{2} \cdot R}{m_{1}+m_{2}}
\end{aligned}
$$
Looking for more such questions to practice?
Download the MARKS App - The ultimate prep app for IIT JEE & NEET with chapter-wise PYQs, revision notes, formula sheets, custom tests & much more.