Question

Find the time period of the motion of the particle shown in figure. Neglect the small effect of the bend near the bottom.

Answer 1

Effective acceleration$=gsin{45}^{\circ }$

for left track,

Distance to move$=100\sqrt{2}ms=ut+\frac{1}{2}a{t}^{2}t=\sqrt{\frac{2\times 100\sqrt{2}}{\frac{10}{\sqrt{2}}}}=\sqrt{40}$

For right track,

$t=\sqrt{\frac{2\times 100\times 2\times 2}{\sqrt{3}\times 10\times \sqrt{3}}}=\sqrt{\frac{80}{3}}$

Total time taken for a period,

$T=(\sqrt{40}+\frac{\sqrt{80}}{3}).2T=\left(\frac{\sqrt{120}+\sqrt{80}}{\sqrt{3}}\right).2$