Each of the four wheels in column I has an outer ring having radius R and mass m . Other than the outer ring the wheels comprise of some uniform rods (each of mass m and length R ) or some lamina (hav

Question

Each of the four wheels in column I has an outer ring having radius R and mass m . Other than the outer ring the wheels comprise of some uniform rods (each of mass $m$ and length $R$ ) or some lamina (having the same mass m ). Column II gives radius of gyration about axis passing through centre of ring perpendicular to its plane.

Column I	Column II
(I)	(P) $R \frac{3}{4}$
(II)	(Q) $R \frac{11}{18}$
(III) One disc + ring	(R) $\frac{R}{2}$
(IV) Outer ring + half disc + one rod	(S) $R \frac{7}{15}$
	(T) $\frac{R}{3}$

TestHub · Accepted Answer

For ( A ) : I = M R 2 + 3 ( 3 M R 2 ​ ) = 2 M R 2 ⇒ K = M I ​ ​ = 4 M 2 M R 2 ​ ​ = 2 ​ R ​ For ( B ) : I = M R 2 + 4 ( 3 M R 2 ​ ) = 3 7 M R 2 ​ ⇒ K = 3 ( 5 M ) 7 M R 2 ​ ​ = R 15 7 ​ ​ For ( C ) : I = M R 2 + 2 1 ​ M R 2 = 2 3 M R 2 ​ ⇒ K = 2 ( 2 M ) 3 M R 2 ​ ​ = R 2 3 ​ ​ For ( D ) : I = M R 2 + 2 1 ​ M R 2 + 3 1 ​ M R 2 = 6 11 ​ M R 2 K = 6 ( 3 M ) 11 M R 2 ​ ​ = R 18 11 ​ ​

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