Two bodies $A$ and $B$ have masses $2\ kg$ and $5\ kg$ respectively. Each one is acted upon by a force of $4\ kg\ wt$. If they acquire the same kinetic energy in times $t_{A}$ and $t_{B}$, then the ratio $\frac{t_{A}}{t_{B}}$ is

Question

Dr. Abubacker · Accepted Answer

(b) According to question, $\frac{1}{2}m_{A}v_{A}^{2} = \frac{1}{2}m_{B}v_{B}^{2}$
$\Rightarrow \frac{v_{A}}{v_{B}} = \sqrt{\frac{m_{B}}{m_{A}}} = \sqrt{\frac{5}{20}} = \frac{1}{2}$
Using Impulse Momentum
$\frac{F\mathrm{\Delta}t_{A}}{F\mathrm{\Delta}t_{B}} = \frac{m_{A}\mathrm{\Delta}v_{A}}{m_{B}\mathrm{\Delta}v_{B}} \Rightarrow \frac{\mathrm{\Delta}t_{A}}{\mathrm{\Delta}t_{B}} = \frac{20}{5} 	imes \frac{1}{2} = 2$

Q. Two bodies $A$ and $B$ have masses $2\ kg$ and $5\ kg$ respectively. Each one is acted upon by a force of $4\ kg\ wt$. If they acquire the same kinetic energy in times $t_{A}$ and $t_{B}$, then the ratio $\frac{t_{A}}{t_{B}}$ is

Explanation

Reviewed by Dr. Abubacker

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