A uniform metal rod of length 1m is clamped at two points 5 cm from one end and 15 cm from the other end. The possible frequencies of the natural oscillations (longitudinal) of the rod can be (Y=1.6×1011 N/m2, ρ=2500 kg/m3)

A uniform metal rod of length 1m is clamped at two points 5 cm from one end and 15 cm from the other end. The possible frequencies of the natural oscillations (longitudinal) of the rod can be (Y=1.6×1011 N/m2, ρ=2500 kg/m3)

Consider regular polygons with number of sides n=3,4,5… as shown in the figure. The center of mass of all the polygons is at height h from the ground. They roll on a horizontal surface about the leading vertex without slipping and sliding as depicted. The maximum increase in height of the locus of the center of mass for each polygon is Δ . Then, Δ depends on n and h as

Consider regular polygons with number of sides n=3,4,5… as shown in the figure. The center of mass of all the polygons is at height h from the ground. They roll on a horizontal surface about the leading vertex without slipping and sliding as depicted. The maximum increase in height of the locus of the center of mass for each polygon is Δ . Then, Δ depends on n and h as