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4-1.Newton's Laws of Motion
medium
A particle of mass $m$ moving with velocity $u$ makes an elastic one dimensional collision with a stationary particle of mass $m$. They are in contact for a very short time $T$. Their force of interaction increases from zero to $F_0$ linearly in time $T/2$, and decreases linearly to zero in further time $T/2$. The magnitude of $F_0$ is
A
$mu/T$
B
$2mu/T$
C
$mu/2T$
D
None of these
Solution
(b) In elastic one dimensional collision particle rebounds with same speed in opposite direction
i.e. change in momentum $ = 2mu$
But Impulse $ = F \times T = $ Change in momentum
$⇒$ ${F_0} \times T = 2mu$ $⇒$ ${F_0} = \frac{{2mu}}{T}$
Standard 11
Physics
