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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. Navjyot Kalra
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