List-I shows four planar structures made of uniform solid rods each of mass m and length l. In the List-II the possible moment of inertia of these structures about an axis OCO', which lies in the plane of the structures, are given. Choose the option that describes the correct match between the entries in List-I to those in List-II.
- P→5, Q→1, R→4, S→2
- P→1, Q→3, R→4, S→2
- P→5, Q→3, R→2, S→1
- P→5, Q→4, R→2, S→1
Answer
(1) P→5, Q→1, R→4, S→2
Solution
Rod of length l with one end on the axis, at angle to it: I = ml23 2 ; a rod parallel to the axis at distance d: I = md2.
(P) Two rods at 45 : 2 ml23 12 = 13ml2 → (5).
(Q) CA, CB at 60 : 2 ml23 34 = ml22; AB at distance 32l: 34ml2; total 54ml2 → (1).
(R) Square about its diagonal: four rods at 45 , each ml26; total 23ml2 → (4).
(S) Two rods at 30 : 2 ml23 14 = 16ml2 → (2).
P→5, Q→1, R→4, S→2
Answer: (A)