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Units And Measurement

Question
CBSEENPH11020609

A small object of uniform density rolls up a curved surface with an initial velocity v'. It reaches up to a maximum height of fraction numerator 3 straight v squared over denominator 4 straight g end fraction with respect to the initial position. The object is,

  • ring

  • solid sphere

  • hollow sphere

  • disc

Solution

D.

disc

As v = square root of fraction numerator 2 gh over denominator 1 plus begin display style straight k squared over straight r squared end style end fraction end root
Given, h = fraction numerator 3 straight v squared over denominator 4 straight g end fraction
straight v squared space equals space fraction numerator 2 gh over denominator 1 space plus space begin display style straight k squared over straight r squared end style end fraction space
space space space space equals space fraction numerator 2 straight g space 3 straight v squared over denominator 4 straight g open parentheses 1 plus begin display style straight k squared over straight r squared end style close parentheses end fraction
space space space space equals space fraction numerator 6 space gv squared over denominator 4 space straight g space open parentheses 1 space plus begin display style straight u squared over straight v squared end style close parentheses end fraction
1 space equals space fraction numerator 3 over denominator 2 space open parentheses 1 plus begin display style straight k squared over straight v squared end style close parentheses end fraction
space space space 1 plus straight k squared over straight r squared space equals space 3 over 2
rightwards double arrow space straight k squared over straight r squared space equals space 3 over 2 space minus space 1 space
space space space space space space space space space space space equals space 1 half
straight k squared space equals space 1 half straight r squared space left square bracket space Equation space of space disc right square bracket
Hence, the object is disc.