Two objects having masses $1: 4$ ratio are at rest. When both of them are subjected to same force separately…

Two objects having masses $1: 4$ ratio are at rest. When both of them are subjected to same force separately, they achieved same kinetic energy during times $t_1$ and $t_2$ respectively. Then ratio of $t_1$ to $t_2$ is
  1. $4$
  2. $2$
  3. $2.5$
  4. $1$

Solution

After time $\mathrm{t}_1$, $\mathrm{k}_1=\frac{1}{2} \mathrm{~m} \mathrm{v}_1^2=\frac{1}{2} \mathrm{~m}\left(\mathrm{at}_1\right)^2=\frac{1}{2} \mathrm{ma}^2 \mathrm{t}_1^2$
After time $t_2$, $\begin{aligned} & \mathrm{k}_2=\frac{1}{2}(4 \mathrm{~m}) \mathrm{v}_2^2=\frac{1}{2}(4 \mathrm{~m})\left(\mathrm{at}_2\right)^2=2 \mathrm{ma}^2 \mathrm{t}_2^2 \\ & \therefore \mathrm{~K}_1=\mathrm{K}_2 \Rightarrow \frac{1}{2} \mathrm{ma}^2 \mathrm{t}_1^2=2 \mathrm{ma}^2 \mathrm{t}_2^2 \quad \therefore \frac{\mathrm{t}_1}{\mathrm{t}_2}=2 \end{aligned}$

Asked in: AP EAMCET 2024 (20 May Shift 2)

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