Question

A uniform rectangular plate $R$ of sides $a$ and $b$ and a uniform square plate $S$ of side $c$ have same masses and areas as shown in the figure.

Then,
$(i)\frac{I_{xR}}{I_{xS}}<1$
$(ii)\frac{I_{yR}}{I_{yS}}>1$
Which of the above relations is correct?

• A. (i) only
• B. (ii) only
• C. Both (i) and (ii)
• D. Neither (i) nor (ii)

Answer 1

Answer: (C)

As, area of rectangular plate $R=$ Area of square plate $S$
$\therefore a\times b=c^2$
$(i)\frac{I_{xR}}{I_{xS}}=\frac{b^2}{c^2}=\frac{b}{a}$
As $b<a$
$\therefore \frac{I_{xR}}{I_{xS}}<1$
$(ii)\frac{I_{yR}}{I_{yS}}=\frac{a^2}{c^2}=\frac{a}{b}$
As $a>b$
$\therefore \frac{I_{yR}}{I_{yS}}>1$