A thin rod of length ‘L’ is lying along the x-axis with its

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 Multiple Choice QuestionsMultiple Choice Questions

11.

A water fountain on the ground sprinkles water all around it. If the speed of water coming out of the fountain is v, the total area around the fountain that gets wet is

  • straight pi straight v to the power of 4 over straight g squared
  • straight pi over 2 straight v to the power of 4 over straight g squared
  • straight pi straight v squared over straight g squared
  • straight pi straight v squared over straight g squared
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12.

A small particle of mass m is projected at an angle θ with the x–axis with an initial velocity v0 in the x–y plane as shown in the figure. At a time t<vosin/g, the angular momentum of the particle is

  • negative mgv subscript straight o space straight t squared space cos space straight theta space bold j with bold hat on top
  • mgv subscript 0 straight t space cos space straight theta space bold k with bold hat on top
  • negative 1 half space mgv subscript 0 straight t squared space cos space straight theta bold space bold k with bold hat on top bold space
  • negative 1 half space mgv subscript 0 straight t squared space cos space straight theta bold space bold k with bold hat on top bold space
821 Views

13.

The moment of inertia of a uniform cylinder of length

  • 1

1287 Views

14.

A slender uniform rod of mass M and length

  • fraction numerator 3 straight g over denominator 2 calligraphic l end fraction space cos space straight theta
  • fraction numerator 2 space straight g over denominator 3 space calligraphic l end fraction space cos space straight theta
  • fraction numerator 3 straight g over denominator 2 space calligraphic l end fraction space sin space straight theta
  • fraction numerator 3 straight g over denominator 2 space calligraphic l end fraction space sin space straight theta
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15.

A thin uniform rod of length

  • 1 third fraction numerator calligraphic l squared straight omega squared over denominator straight g end fraction
  • 1 over 6 fraction numerator calligraphic l straight omega over denominator straight g end fraction
  • 1 half fraction numerator calligraphic l squared straight omega squared over denominator straight g end fraction
  • 1 half fraction numerator calligraphic l squared straight omega squared over denominator straight g end fraction
251 Views

16.

Let P(r) = Qr/πR4 be the charge density distribution for a solid sphere of radius R and total charge Q. for a point ‘p’ inside the sphere at distance r1 from the centre of the sphere, the magnitude of electric field is

  • fraction numerator straight Q over denominator 4 πε subscript straight o straight r subscript 1 superscript 2 end fraction
  • 0

  • fraction numerator Qr subscript 1 superscript 2 over denominator 4 πε subscript straight o straight R to the power of 4 end fraction
  • fraction numerator Qr subscript 1 superscript 2 over denominator 4 πε subscript straight o straight R to the power of 4 end fraction
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17.

A thin rod of length ‘L’ is lying along the x-axis with its ends at x = 0 and x = L. Its linear density (mass/length) varies with x as,straight k space open parentheses straight x over straight L close parentheses to the power of straight n where n can be zero or any positive number. If the position xCM of the centre of mass of the rod is plotted against ‘n’, which of the following graphs best approximates the dependence of xCM on n? 


A.

space straight x subscript cm space equals space fraction numerator integral dmx over denominator integral dm end fraction
fraction numerator integral begin display style λdx end style begin display style. end style begin display style straight x end style over denominator integral begin display style dm end style end fraction
space equals space fraction numerator integral begin display style straight k end style begin display style begin display style open parentheses straight x over straight L close parentheses end style squared end style begin display style. end style begin display style xdx end style over denominator straight k open parentheses begin display style straight x over straight L end style close parentheses to the power of straight n space dx end fraction
space equals space open square brackets fraction numerator begin display style fraction numerator kx to the power of straight n plus 2 end exponent over denominator left parenthesis straight n plus 2 right parenthesis straight L to the power of straight n end fraction end style over denominator begin display style fraction numerator kx to the power of straight n plus 1 end exponent over denominator left parenthesis straight n plus 1 right parenthesis straight L to the power of straight n end fraction end style end fraction close square brackets subscript 0 superscript straight L
space equals space open square brackets fraction numerator straight x left parenthesis straight n plus 1 right parenthesis over denominator straight n plus 2 end fraction close square brackets subscript 0 superscript straight L
straight x subscript cm space equals space straight L over 2 comma fraction numerator 2 straight L over denominator 3 end fraction comma fraction numerator 4 straight L over denominator 5 end fraction comma fraction numerator 5 straight L over denominator 6 end fraction comma.....
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18.

Consider a uniform square plate of side ‘a’ and mass ‘m’. The moment of inertia of this plate about an axis perpendicular to its plane and passing through one of its corners is

  • (5/6)ma2

  • (1/12)ma2

  • (7/12)ma2

  • (7/12)ma2

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19.

A circular disc of radius R is removed from a bigger circular disc of radius 2R such that the circumferences of the discs coincide. The centre of mass of the new disc is α/R from the centre of the bigger disc.The value of α is

  • 1/3

  • 1/2

  • 1/6

  • 1/6

313 Views

20.

A round uniform body of radius R, mass M and moment of inertia ‘I’, rolls down (without slipping) an inclined plane making an angle θ with the horizontal. Then its acceleration is

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