IIT-JEE-Physics-2006

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5.     Given a sample of Radium-226 having half-life of 4 days. Find the probability, a nucleus distintegrates after 2 half lives.

        (A)    1

        (B)    ½

        (C)    1.5

        (D)    ¾

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

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) is 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

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 are the time periods of masses m_A and m_Brespectively, then

        (A)   T_A/T_B =(r_A/r_B )^3/2

        (B)    T_A > T_B (if r_A > r_B)

        (C)    T_A > T_B (if m_A > m_B)

        (D)    T_A = T_B

9.     A solid sphere of mass M, radius R and having moment of inertia about an axis passing through the centre of mass as I, is recast into a disc of thickness t, whose moment of inertia about an axis passing through its edge and perpendicular to its plane remains I. Then, radius of the disc will be

        (A) 2R/√15

        (B) R√(2/15)

        (C) 4R/√15

        (D) R/4

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