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