Question

Find the centre of mass of letter 'F' which is cut from a uniform metal sheet from point A.

Answer 1

Given that,

The letter 'F' which is cut from a uniform metal sheet from point A.

According to this figure,

The figure is divided in three parts.

Suppose, the mass per area of sheet is σ

$\sigma=\dfrac{m}{A}$

The mass of sheet will be

$m=\sigma\times A$

We need to calculate the center of mass of letter F in x axis

Using formula of center of mass

$X_{cm}=\dfrac{m_{1}x_{1}+m_{2}x_{2}+m_{3}x_{3}}{m_{1}+m_{2}+m_{3}}$

Put the value into the formula

$X_{cm}=\dfrac{\sigma\times6\times2\times3+\sigma\times2\times6\times1+\sigma\times2\times2\times3}{\sigma\times2\times6+\sigma\times2\times6+\sigma\times2\times2}$

$X_{cm}=\dfrac{15}{7}$

We need to calculate the center of mass of letter F in y axis

Using formula of center of mass

$Y_{cm}=\dfrac{m_{1}y_{1}+m_{2}y_{2}+m_{3}y_{3}}{m_{1}+m_{2}+m_{3}}$

Put the value into the formula

$Y_{cm}=\dfrac{\sigma\times6\times2\times1+\sigma\times2\times6\times5+\sigma\times2\times2\times5}{\sigma\times2\times6+\sigma\times2\times6+\sigma\times2\times2}$

$Y_{cm}=\dfrac{23}{7}$

Hence, The centre of mass of letter 'F' is $\dfrac{15}{7},\dfrac{23}{7}$

(2) is correct option

Answer 2

Answer:

15/7,33/7

Explanation: