physice06

# physice06 - IIT-JEE2006-PH-1 FIITJEE Solutions to...

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FIITJEE Ltd. ICES House, 29-A, Kalu Sarai, Sarvapriya Vihar New Delhi - 16, Ph : 2686 5182, 26965626, 2685 4102, 26515949 Fax : 26513942 IIT-JEE2006-PH-1 FIITJEE Solutions to IITJEE–2006 P P h h y y s s i i c c s s Time: 2 hours Note: The marking Scheme is (+3, 1) for question numbers 1 to 12 , (+5, 1) for question numbers 13 to 20, (+5, 2) for question numbers 21 to 32 and (+6, 0) for question numbers 33 to 40. 1 Given, R 1 = 1 C 1 = 2 µ F R 2 = 2 C 2 = 4 µ F C 1 C 2 R 1 R 2 V (I) C 2 C 1 R 1 R 2 V C 2 C 1 R 2 R V (II) (III) The time constants (in µ S) for the circuits I, II, III are respectively (A) 18, 8/9, 4 (B) 18, 4, 8/9 (C) 4, 8/9, 18 (D) 8/9, 18, 4 Sol. (D) τ 1 = 8/9 µ S τ 2 = 18 µ S τ 3 = 4 µ S 2. Two blocks A and B of masses 2m and m, respectively, are connected by a massless and inextensible string. The whole system is suspended by a massless spring as shown in the figure. The magnitudes of acceleration of A and B, immediately after the string is cut, are respectively (A) g, g/2 (B) g/2, g (C) g , g (D) g/2, g/2 A 2m B m Sol. (B) a A = g/2 a B = g 3 mg 2 mg A B mg 3. A point object is placed at a distance of 20 cm from a thin plano-convex lens of focal length 15 cm, if the plane surface is silvered. The image will form at (A) 60 cm left of AB (B) 30 cm left of AB (C) 12 cm left of AB (D) 60 cm right of AB Sol. (C) 121 1 5 F Ff 2 =+⇒= A 15 cm 20 cm L O A B 211 15 v 20 −=− v = 12 cm i.e.12 cm left of AB

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FIITJEE Ltd. ICES House, 29-A, Kalu Sarai, Sarvapriya Vihar New Delhi - 16, Ph : 2686 5182, 26965626, 2685 4102, 26515949 Fax : 26513942 IIT-JEE2006-PH-2 4. A biconvex lens of focal length f forms a circular image of sun of radius r in focal plane. Then (A) π r 2 f (B) π r 2 f 2 (C) if lower half part is covered by black sheet, then area of the image is equal to π r 2 /2 (D) if f is doubled, intensity will increase Sol. (B) r = f tan α Hence, π r 2 f 2 θ α r + 5. Given a sample of Radium-226 having half-life of 4 days. Find the probability, a nucleus disintegrates after 2 half lives. (A) 1 (B) 1/2 (C) 1.5 (D) 3/4 Sol. (B) Disintegration of each nuclei is independent of any factor. Hence, each nuclei has same chance of disintegration. 6. Graph of position of image vs position of point object from a convex lens is shown. Then, focal length of the lens is (A) 0.50 ± 0.05 cm (B) 0.50 ± 0.10 cm (C) 5.00 ± 0.05 cm (D) 5.00 ± 0.10 cm 10 30 v cm u cm 20 0 10 ( 9, +9) 31 30 31 Sol. (D) 111 fvu =− f = 5 cm f = uv uv + fuv u v ∆+∆ ∆∆∆ =++ + f = 0.15 (for f = 5 cm) The most appropriate answer is 5.00 ± 0.10 cm 7. A massless rod is suspended by two identical strings AB and CD of equal length. A block of mass m is suspended from point O such that BO is equal to ‘x’. Further, it is observed that the frequency of 1 st harmonic (fundamental frequency) in AB is equal to 2 nd harmonic frequency in CD. Then, length of BO is (A) L/5 (B) 4L/5 (C) 3L/4 (D) L/4 x m O L B A C D
FIITJEE Ltd. ICES House, 29-A, Kalu Sarai, Sarvapriya Vihar New Delhi - 16, Ph : 2686 5182, 26965626, 2685 4102, 26515949 Fax : 26513942 IIT-JEE2006-PH-3 Sol. (A) 12 1T 1T 2 = µµ AA T 2 = T 1 /4 For rotational equilibrium, T 1 x = T 2 (L x) x = L/5 m O B A C D T 2 T 1 8. A system of binary stars of masses m A and m B are moving in circular orbits of radii r A and r B respectively. If T A and T B

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## This note was uploaded on 06/27/2008 for the course PHY 101 taught by Professor Wormer during the Spring '08 term at New School.

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physice06 - IIT-JEE2006-PH-1 FIITJEE Solutions to...

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