An object of mass 500 ; g, intitally at rest acted upon by a vari… - Vidyadip

MCQ

An object of mass $500\; \mathrm{g}$, intitally at rest acted upon by a variable force where $\mathrm{X}$ component varies with $\mathrm{X}$ in the manner shown. The velocities of the object at point $X=8 \;\mathrm{m}$ and $X=12\; \mathrm{m},$ would be the respective values

A
$18 \;\mathrm{m} / \mathrm{s}$ and $24.4 \;\mathrm{m} / \mathrm{s}$
B
$23 \;\mathrm{m} / \mathrm{s}$ and $24.4 \;\mathrm{m} / \mathrm{s}$
✓
$23 \;\mathrm{m} / \mathrm{s}$ and $20.6 \;\mathrm{m} / \mathrm{s}$
D
$18 \;\mathrm{m} / \mathrm{s}$ and $20.6 \;\mathrm{m} / \mathrm{s}$

✓

Answer

Correct option: C.

$23 \;\mathrm{m} / \mathrm{s}$ and $20.6 \;\mathrm{m} / \mathrm{s}$

c
${W}={\Delta K E}$

At $x=8\;;\;130=\frac{1}{2}\left(\frac{1}{2}\right) v^{2}$

$\Rightarrow v=2 \sqrt{130}=22.8 \mathrm{ms}^{-1}$

For $\mathrm{v}=20.6 \mathrm{ms}^{-1}$

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