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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