A particle of mass 10 g moves in a straight line with retardation , where is the displacement in SI units. Its loss of kinetic energy for above displacement is The value of will be _________ . [2023]

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Solution

Q.
A particle of mass 10 g moves in a straight line with retardation $2 x$ , where $x$ is the displacement in SI units. Its loss of kinetic energy for above displacement is ${(\frac{10}{x})}^{- n} J .$ The value of $n$ will be _________ . [2023]

Ans.
(2)

$Loss of K.E. = work done against retarding force$

$= \int_{0}^{x} m a d x = \int_{0}^{x} m 2 x d x = m x^{2}$

$= (10^{- 2} kg) x^{2} J = {(\frac{10}{x})}^{- 2} J$

$So n = 2$

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