Laws of Motion

  • Question 497
    CBSEENPH11020427

    An annular ring with inner and outer radii R1 and R2 is rolling without slipping with a uniform angular speed. The ratio of the forces experienced by the two particles situated on the inner and outer parts of the ring, F1/F2 is

    • R1/R2

    • (R1/R2)2

    • 1

    • R2/R1

    Solution

    A.

    R1/R2

    straight F subscript 1 over straight F subscript 2 space equals space fraction numerator straight R subscript 1 straight omega squared over denominator straight R subscript 2 straight omega squared end fraction space equals straight R subscript 1 over straight R subscript 2
    Question 498
    CBSEENPH11020428

    A smooth block is released at rest on a 45° incline and then slides a distance d. The time taken to slide is n times as much to slide on rough incline than on a smooth incline. The coefficient of friction is

    • straight mu subscript straight k space equals space 1 minus 1 over straight n squared
    • straight mu subscript straight k space equals space square root of 1 minus 1 over straight n squared end root
    • straight mu subscript straight s space equals space 1 minus 1 over straight n squared
    • straight mu subscript s space equals space square root of 1 minus 1 over straight n squared end root

    Solution

    A.

    straight mu subscript straight k space equals space 1 minus 1 over straight n squared straight d space equals space 1 half fraction numerator straight g over denominator square root of 2 end fraction straight t subscript 1 superscript 2
straight d equals space 1 half fraction numerator straight g over denominator square root of 2 end fraction left parenthesis 1 minus straight mu subscript straight k right parenthesis straight t subscript 2 superscript 2
fraction numerator straight t subscript 2 superscript 2 over denominator straight t subscript 1 superscript 2 end fraction space equals space straight n squared space equals fraction numerator 1 over denominator 1 minus straight mu subscript straight k end fraction
    Question 499
    CBSEENPH11020429

    The upper half of an inclined plane with inclination φ is perfectly smooth while the lower half is rough. A body starting from rest at the top will again come to rest at the bottom if the coefficient of friction for the lower half is given by

    • 2sinφ

    • 2cosφ

    • 2tanφ
    • tanφ

    Solution

    C.

    2tanφ
    Question 500
    CBSEENPH11020430

    A bullet fired into a fixed target loses half of its velocity after penetrating 3 cm. How much further it will penetrate before coming to rest assuming that it faces constant resistance to motion?

    • 3.0 cm

    • 2.0 cm

    • 1.5 cm

    • 1.0 cm

    Solution

    D.

    1.0 cm

    straight F.3 space equals 1 half mv squared minus 1 half straight m straight v squared over 4
straight F left parenthesis 3 plus straight x right parenthesis space equals 1 half mv squared
space straight x space equals space 1 space cm

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