A particle of mass 10 gm moves in a field where potential energy per unit mass is given by expression U=8 × 104 x2 erg / gm . If the total energy of the particle is 8 × 107 erg then the relation between x and time t is:[φ= constant ]

Question

A particle of mass 10 gm moves in a field where potential energy per unit mass is given by expression U=8 × 104 x2 erg / gm . If the total energy of the particle is 8 × 107 erg then the relation between x and time t is:[φ= constant ] (A) x=10 sin (400 t+φ) cm (B) x= sin (400 t+φ) m (C) x=10 sin (40 t+φ) cm (D) x=100 sin (4 t+φ) m

Tardigrade Admin · Accepted Answer

Potential energy per unit mass of a particle is given as (1 / 2) ω2 x2 and equating the given value with this expression we get the value of ω=400 rad / s and Total energy is (1/2) ω2 A2 which gives the amplitude 10 cm.

Q. A particle of mass $10 g m$ moves in a field where potential energy per unit mass is given by expression $U = 8 \times 1 0^{4} x^{2} er g / g m .$ If the total energy of the particle is $8 \times 1 0^{7}$ erg then the relation between $x$ and time $t$ is: $[ϕ =$ constant $]$

$x = 10 sin (400 t + ϕ) c m$

$x = sin (400 t + ϕ) m$

$x = 10 sin (40 t + ϕ) c m$

$x = 100 sin (4 t + ϕ) m$

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

Q. A particle of mass 10gm moves in a field where potential energy per unit mass is given by expression U=8×104x2erg/gm. If the total energy of the particle is 8×107 erg then the relation between x and time t is:[ϕ= constant ]

x=10sin(400t+ϕ)cm

x=sin(400t+ϕ)m

x=10sin(40t+ϕ)cm

x=100sin(4t+ϕ)m