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

C.

straight pi straight v squared over straight g squared

Maximum range of water coming out of the fountain

straight R subscript straight m space equals space straight v squared over straight g
therefore comma space Total space area space around space fountain
space straight A space equals space πR subscript straight m superscript 2 space equals straight pi straight v to the power of 4 over straight g squared

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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

D.

1 half fraction numerator calligraphic l squared straight omega squared over denominator straight g end fraction 1 half open parentheses fraction numerator straight m space calligraphic l squared over denominator 3 end fraction close parentheses straight omega squared space equals space mgh
rightwards double arrow space straight h space equals space fraction numerator straight omega squared calligraphic l squared over denominator 6 straight g end fraction
251 Views

The moment of inertia of a uniform cylinder of length

  • 1


C.

1287 Views

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

C.

fraction numerator 3 straight g over denominator 2 space calligraphic l end fraction space sin space straight theta

Taking torque about pivot τ = Iα
mg space sin space straight theta space calligraphic l over 2 space equals space fraction numerator straight m calligraphic l squared over denominator 3 end fraction space straight alpha
straight alpha space equals space fraction numerator 3 straight g over denominator 2 space calligraphic l end fraction space sinθ
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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


C.

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

The angular momentum  of the projectile is given by,
L = m (r x v)
straight L space equals space straight m space left square bracket space straight v subscript 0 space cos space straight theta space straight t space bold i with hat on top space plus space left parenthesis straight v subscript 0 space sin space straight theta space minus space gt right parenthesis bold j with hat on top right square bracket
space space space space space space space space space space space space space straight x space left square bracket space straight v subscript straight o space cos space straight theta space straight t space bold i with hat on top space plus space left parenthesis straight v subscript 0 space sin space straight theta minus space gt right parenthesis bold j with hat on top right square bracket
equals space mv subscript 0 space cos space θt space open square brackets negative 1 half gt close square brackets bold space bold k with bold hat on top
bold space bold equals space minus 1 half space mgv subscript 0 space straight t squared space cos space straight theta bold space bold k with bold hat on top

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