Question

A particle of mass m is executing oscillation about the origin on x-axis. Its potential energy is U(x) = k|x|³ where k is force constant. If time period of particle depends upon amplitude of oscillation 'a', mass of particle 'm' and force constant 'k', then time period is proportional to –

• A. $\frac{1}{\sqrt{a}}$
• B. $\frac{1}{a}$
• C. $\sqrt{a}$
• D. a^3/2

Answer 1

Answer: (A)

$\frac{1}{\sqrt{a}}$

Answer 2

[k] = $\frac{\lbrack U\rbrack}{\lbrack x\rbrack^{3}}$ $= \text{ M}\text{L}^{\text{-1}}T^{\text{-2}}\$

T µ k^x

µ a^y

µ m^z

$\Rightarrow T = K'k^{x}a^{y}m^{z}$

Ž x = –1/2