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प्रश्न
In an elastic collision
पर्याय
the initial kinetic energy is equal to the final kinetic energy
the final kinetic energy is less than the initial kinetic energy
the kinetic energy remains constant
the kinetic energy first increases then decreases.
उत्तर
the final kinetic energy is less than the initial kinetic energy
As some energy is loss into heat in an inelastic collision, the final kinetic energy is less than the initial kinetic energy.
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संबंधित प्रश्न
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- ring, and
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Consider the following two statements:
(A) Linear momentum of the system remains constant.
(B) Centre of mass of the system remains at rest.
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(c) the density decreases from left to right upto the centre and then increases
(d) the density increases from left to right upto the centre and then decreases.
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(a) v0 = 0, a0 = 0
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In an elastic collision
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[Hint : The light rod will exert a force on the ball B
only along its length.]
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- Show pi = p’i + miV Where pi is the momentum of the ith particle (of mass mi) and p′ i = mi v′ i. Note v′ i is the velocity of the ith particle relative to the centre of mass. Also, prove using the definition of the centre of mass `sum"p""'"_"t" = 0`
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Show K = K′ + 1/2MV2
where K is the total kinetic energy of the system of particles, K′ is the total kinetic energy of the
system when the particle velocities are taken with respect to the centre of mass and MV2/2 is the
kinetic energy of the translation of the system as a whole (i.e. of the centre of mass motion of the
system). The result has been used in Sec. 7.14. - Show where `"L""'" = sum"r""'"_"t" xx "p""'"_"t"` is the angular momentum of the system about the centre of mass with
velocities taken relative to the centre of mass. Remember `"r"_"t" = "r"_"t" - "R"`; rest of the notation is the standard notation used in the chapter. Note L′ and MR × V can be said to be angular momenta, respectively, about and of the centre of mass of the system of particles. - Show `"dL"^"'"/"dt" = ∑"r"_"i"^"'" xx "dP"^"'"/"dt"`
Further show that `"dL"^'/"dt" = τ_"ext"^"'"`
Where `"τ"_"ext"^"'"` is the sum of all external torques acting on the system about the centre of mass.
(Hint: Use the definition of centre of mass and third law of motion. Assume the internal forces between any two particles act along the line joining the particles.)
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