Question

Variation of force $F$ acting on a body with time $t$ is as shown in figure. Change in momentum of the body in the interval $4\text{s}$ to $8\text{s}$ is

• A. $10{\text{kg ms}}^{-1}$
• B. $5{\text{kg ms}}^{-1}$
• C. $100{\text{kg ms}}^{-1}$
• D. $20{\text{kg ms}}^{-1}$

Answer 1

The correct option is D $20{\text{kg ms}}^{-1}$

Change in momentum is area under curves.
due to similarity of triangles
$\frac{20}{8}=\frac{F}{4}\Rightarrow F=10\text{N}$
Area of shaded region
$\Rightarrow \frac{1}{2}\times 4\times F$
$=\frac{1}{2}\times 4\times 10$

$=20\text{N.s}$ where $\text{Ns}$ is derived SI unit of impulse or we call it as change in momentum, it is dimensionally equivalent to ${\text{kg ms}}^{-1}$