An object of mass 500 g, initially at rest, is acted upon by a va…

MCQ

An object of mass 500 g, initially at rest, is acted upon by a variable force whose X-component varies with X in the manner shown. The velocities of the object at the points X = 8 m and X = 12 m, would have the respective values of

A
18m/s and 20.6 m/s
B
18 m/s and 24.4 m/s
C
23 m/s and 24.4 m/s
D
23 m/s and 20.6 m/s

✓

Answer

Hint: From work-energy theorem
∆ K.E. = work = area under F-x graph
From x = 0 to x = 8m
$\frac{1}{2} mv ^2=(5 \times 20)+(3 \times 10)$
$\therefore \frac{1}{2} m v^2=100+30$
$\begin{array}{ll}\therefore & v ^2=520 \\ \therefore &
v =\sqrt{520}=22.8 \approx 23 m / s \end{array}$
Similarly, from $x=0$ to $x=12 m$
$\frac{1}{2} mv ^2=100+30-47.5+20$
$\therefore \quad \frac{1}{2} mv ^2=102.5$
$\therefore \quad v ^2=\frac{2 \times 102.5}{0.5}$
$\therefore \quad v =\sqrt{410} \approx 20.6 m / s$
23 m/s and 20.6 m/s

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