JEE Main · 2004 · 24 Apr 2004 · Offline · Work, Power & Energy

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A particle moves in a straight line with retardation proportional to its displacement. Its loss of kinetic energy for any displacement x is proportional to

(A) $x^{2}$ ✓ Correct
(B) $e^{x}$
(C) $x$
(D) $lo g_{e} x$

Answer: (A)

Solution

Since the retardation builds up in proportion to the distance covered, write it as

a = - k x

with

k

a positive constant. The retarding force then does work

\int F d x = \int m (- k x) d x = - \frac{1}{2} mk x^{2}

as the particle advances through

x

, and by the work-energy theorem this is exactly the change in kinetic energy. The loss of kinetic energy therefore varies as

x^{2}

JEE Main · 2004 · 24 Apr 2004 · Offline · Single correct option

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