The potential energy of a particle is given by the expression U ( x )=-α x +β sin ( x /γ) . A dimensionless combination of the constants α, β and γ is :-

Question

The potential energy of a particle is given by the expression U ( x )=-α x +β sin ( x /&gamma;) . A dimensionless combination of the constants α, β and &gamma; is :- (A) (α/β &gamma;) (B) (α2/β α) (C) (&gamma;/α β) (D) (α &gamma;/β)

Tardigrade Admin · Accepted Answer

[( x /&gamma;)] is dimensionless but [αx]=[β] so [x]=[(β/α)] Therefore [(β/α &gamma;)] or [(α &gamma;/β)] is dimensionless combined

Q. The potential energy of a particle is given by the expression $U (x) = - αx + β sin \frac{x}{γ} .$ A dimensionless combination of the constants $α, β$ and $γ$ is :-

$\frac{α}{β γ}$

$\frac{α ^{2}}{β α}$

$\frac{γ}{α β}$

$\frac{α γ}{β}$

$[\frac{x}{γ}]$ is dimensionless
but $[α_{x}] = [β]$ so $[x] = [\frac{β}{α}]$
Therefore $[\frac{β}{α γ}]$ or $[\frac{α γ}{β}]$ is dimensionless combined

Q. The potential energy of a particle is given by the expression U(x)=−αx+βsinγx​. A dimensionless combination of the constants α,β and γ is :-

βγα​

βαα2​

αβγ​

βαγ​