A rectangular slab ABCD have dimensions a×2a as shown in figure. Match the following two columns List –I List -IIa)Radius of gyration about axis -1p)a12b)Radius of gyration about axis-2q)2a3c)Radius of gyration about axis-3r)a3d)Radius of gyration about axis -4s)4a3 t)a43

a → q , b → r , c → r , d → p

a → q , b → r , c → r , d → p

a → q , b → s , c → p , d → r

a → p , b → s , c → q , d → r

a → q , b → r , c → s , d → p

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A rectangular slab ABCD have dimensions a×2a as shown in figure. Match the following two columns
List –I List -II
a) Radius of gyration about axis -1 p) $\frac{a}{\sqrt{12}}$
b) Radius of gyration about axis-2 q) $\frac{2 a}{\sqrt{3}}$
c) Radius of gyration about axis-3 r) $\frac{a}{\sqrt{3}}$
d) Radius of gyration about axis -4 s) $\frac{4 a}{\sqrt{3}}$
t) $\frac{a}{4 \sqrt{3}}$

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$a \to q, b \to r, c \to r, d \to p$

$a \to q, b \to s, c \to p, d \to r$

$a \to p, b \to s, c \to q, d \to r$

$a \to q, b \to r, c \to s, d \to p$

answer is A.

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a) $K = \sqrt{I / m}$

$= \sqrt{\frac{m {(2 a)}^{2}}{3}} = \frac{2}{\sqrt{3}} a$

b) $K = \sqrt{\frac{m {(2 a)}^{2}}{12}} = \frac{a}{\sqrt{3}}$

c) $K = \sqrt{\frac{m a^{2}}{3}} = \frac{a}{\sqrt{3}}$

d) $K = \sqrt{\frac{m a^{2}}{12}} = \frac{a}{\sqrt{12}}$

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	List –I		List -II
a)	Radius of gyration about axis -1	p)	$\frac{a}{\sqrt{12}}$
b)	Radius of gyration about axis-2	q)	$\frac{2 a}{\sqrt{3}}$
c)	Radius of gyration about axis-3	r)	$\frac{a}{\sqrt{3}}$
d)	Radius of gyration about axis -4	s)	$\frac{4 a}{\sqrt{3}}$
		t)	$\frac{a}{4 \sqrt{3}}$