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The answer to each of the questions is a single digit integer ranging from 0 to 9. A particle of mass m is executing oscillations about the origin on the x-axis. Its potential energy is U(x) = K|x| 3 , where K is a positive constant. If the amplitude of oscillation is a, then its time period T is proportional to a –p/q . Find the value of p + q.



The answer to each of the questions is a single digit integer ranging from 0 to 9.


 





A particle of mass m is executing oscillations about the origin on the x-axis. Its potential energy is U(x) = K|x|3, where K is a positive constant. If the amplitude of oscillation is a, then its time period T is proportional to a–p/q. Find the value of p + q.



 

Grade:10

1 Answers

Navjyot Kalra
askIITians Faculty 654 Points
7 years ago

3

 

        U(x) = K|x|3

 

        \ [K] =

 

        Now time period may depend on T µ (mass)x (amplitude)y (K)z

 

        Or [M0L0T] = [M]x[L]y[ML–1T–2]z = [Mx+zLy–zT–2z]

 

        Equating the powers, we get – 2z = 1 or z =

 

        y – z = 0 or y = z =

 

        \ T µ (amplitude)–1/2 or T µ (a)–1/2 or T µ .

 

        On comparing we get, p = 1, q = 2.

 

        \ p + q = 1 + 2 = 3

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