Question

A particle of mass $10 \,gm$ moves in a field where potential energy per unit mass is given by expression $U=8 \times 10^{4} x^{2} erg / gm .$ If the total energy of the particle is $8 \times 10^{7}$ erg then the relation between $x$ and time $t$ is:$[\phi=$ constant $]$

• A. $x=10 \sin (400 t+\phi) cm$
• B. $x=\sin (400 t+\phi) m$
• C. $x=10 \sin (40 t+\phi) cm$
• D. $x=100 \sin (4 t+\phi) m$

Answer 1

Answer: (A)

Potential energy per unit mass of a particle is given as $(1 / 2) \omega^{2} x^{2}$ and equating the given value with this expression we get the value of $\omega=400\, rad / s$ and Total energy is (1/2) $\omega^{2} A^{2}$ which gives the amplitude $10 \,cm$.