Exam

JEE Main

Year

2024

Date

8 April

Shift

Morning Shift

Subject

Physics

Chapter

Center of Mass, Momentum and Collision

JEE Main 2024 · 8 April · Morning Shift · Physics · Center of Mass, Momentum and Collision

A uniform thin metal plate of mass 10 ~kg with dimensions is shown....

A uniform thin metal plate of mass $10 \mathrm{~kg}$ with dimensions is shown. The ratio of $\mathrm{x}$ and $\mathrm{y}$ coordinates of center of mass of plate in $\frac{n}{9}$. The value of $n$ is ________

Step-by-step solution

$\mathrm{m}_1=\sigma \times 5=10 \mathrm{Kg}$

$$\begin{aligned} & \Rightarrow \mathrm{m}_1 \mathrm{x}_1+\mathrm{m}_2 \mathrm{x}_2=\mathrm{m}_3 \mathrm{x}_3 \\ & 10 \mathrm{x}_1+2(1.5)=12(1.5) \Rightarrow \mathrm{x}_1=1.5 \mathrm{~cm} \\ & \Rightarrow \mathrm{m}_1 \mathrm{y}_1+\mathrm{m}_2 \mathrm{y}_2=\mathrm{m}_3 \mathrm{y}_3 \\ & 10 \mathrm{y}_1+2(1.5)=12 \times 1 \Rightarrow \mathrm{y}_1=0.9 \mathrm{~cm} \\ & \frac{\mathrm{x}_1}{\mathrm{y}_1}=\frac{1.5}{0.9}=\frac{15}{9} \\ & \mathrm{n}=15\end{aligned}$$