Laws of Motion - Result Question 2
2. The force ’ $F$ ’ acting on a particle of mass ’ $m$ ’ is indicated by the force-time graph shown below. The change in momentum of the particle over the time interval from zero to $8 s$ is :
[2014]
(a) $24 Ns$
(b) $20 Ns$
(c) $12 Ns$
(d) $6 Ns$
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Answer:
Correct Answer: 2. (c)
Solution:
- (c) Change in momentum,
$ \begin{aligned} \Delta p & =\int \text{ Fdt } \\ & =\text{ Area of F-t graph } \\ & =\text{ ar of } \Delta-\text{ ar of } \square+\text{ ar of } \square \\ & =\frac{1}{2} \times 2 \times 6-3 \times 2+4 \times 3=12 N-s \end{aligned} $
According to Newton’s 2nd law. $F \propto \frac{d \vec{p}}{d t} \Rightarrow F$ $=K \frac{d \vec{p}}{d t}$ or, $F=\frac{d \vec{p}}{d t}[\because k=1$ in S.I & CGS system $]$ And $d \vec{p}=\vec{F} d t$
