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Q.

A particle moves in a straight line. If u is the velocity at a distance x from a fixed point on the line and v2=a-bx2,where a and b arc constants, then:(i) the motion continues along the positive r-direction only(ii) the motion is simple harmonic(iii) the particle oscillates with a frequency equal to b2π(iv) the total energy of the particle is ma

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a

(i, ii)

b

(ii, iii)

c

(iii, iv)

d

(ii, iv)

answer is B.

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Detailed Solution

v2=a-bx2⇒2v dv=0-b(2x  dx) ⇒                    vdvdx=-bx ⇒                   d2xdx2+bx=0 ⇒ motion is SHM and ω2=b⇒f=ω2π=22π
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