Determine the time period of the particle's motion as depicted in the figure. Disregard the minor effect of the bend near the bottom.

Step-by-step solution

The time taken by the particle to slide down an incline of angle from a height h is given by t = 2s a , where s = h and a = g . Thus, t = 2h g ^2 = 1 2h g . The total time period T of the motion consists of sliding down the first incline, sliding up the second incline, sliding down the second incline, and sliding up the first incline. Therefore, T = 2(t₁ + t₂) = 2 2h g ( 1 ₁ + 1 ₂ ) . Given h = 10 cm = 0.1 m , ₁ = 45^ , ₂ = 60^ , and taking g = 9.8 m/s ^2 : T = 2 2 0.1 9.8 ( 1 45^ + 1 60^ ) T = 2 1 49 ( 2 + 2 3 ) T