Physics - Rotation Question with Solution | TestHub

Key Idea According to conservation of energy, potential energy at height $h=$ kinetic energy at ground. Potential energy = Kinetic energy ie, $$mgh=\frac{1}{2}m{v}^2$$ $$\Rightarrow v=\sqrt{2gh}$$ If $h_1$ and $h_2$ are initial and final heights, then $$v_1=\sqrt{2g{h}_1},v_2=\sqrt{2g{h}_2}$$ Loss in velocity $$\Delta v=v_1-v_2=\sqrt{2g{h}_1}-\sqrt{2g{h}_2}$$ $\therefore$ Fractional loss in velocity $=\frac{\Delta v}{v_1}$ $$\begin{array}{l}=\frac{\sqrt{2g{h}_1}-\sqrt{2g{h}_2}}{\sqrt{2g{h}_1}}\\ =1-\sqrt{\frac{h_2}{h_1}}\end{array}$$ Substituting the values, we have $\therefore$ $$\frac{\Delta v}{v_1}=1-\sqrt{\frac{1.8}{5}}$$ $$\begin{array}{l}=1-\sqrt{0.36}=1-0.6\\ =0.4=\frac{2}{5}\end{array}$$