Question
Consider two waves passing through the same string. Principle of superposition for displacement says that the net displacement of a particle on the string is sum of the displacements produced by the two waves individually. Suppose we state similar principles for the net velocity of the particle and the net kinetic energy of the particle. Such a principle will be valid for
Answer: Option B
:
B
According to principle of super position
⃗ynet=→y1+→y2
Here y1&y2 are particle displacement vectors
differentiating with respect to time.
d⃗ynetdt=d→y1dt+d→y2dt
⃗vnet=⃗v1+⃗v2
Here velocities are vectors.
So yes the superposition law is applicable to velocities.
Now let us square both sides
(vnet)2=(⃗v1+⃗v2)2
v2net=v12+v22+2v1v2 (all are magnitudes)
So clearly the law of super position is not applicable for net kinetic energy.
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:
B
According to principle of super position
⃗ynet=→y1+→y2
Here y1&y2 are particle displacement vectors
differentiating with respect to time.
d⃗ynetdt=d→y1dt+d→y2dt
⃗vnet=⃗v1+⃗v2
Here velocities are vectors.
So yes the superposition law is applicable to velocities.
Now let us square both sides
(vnet)2=(⃗v1+⃗v2)2
v2net=v12+v22+2v1v2 (all are magnitudes)
So clearly the law of super position is not applicable for net kinetic energy.
Was this answer helpful ?
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