A weight of 500N is supported by two metallic ropes as shown in the figure. The values of tensions T₁ and T₂ are respectively.

A small ball of mass 1 kg moving with a velocity of 12 m/s undergoes a direct central impact with a stationary ball of mass 2 kg. The impact is perfectly elastic. The speed (in m/s) of 2 kg mass ball after the impact will be ____________

Two identical trusses support a load of 100 N as shown in the figure. The length of each truss is 1.0m; cross-sectional area is 200 mm² ; Young’s modulus E = 200GPa. The force in the truss AB (in N) is _____ .

In a statically determinate plane truss, the number of joints $$(j)$$ and the number of members $$(m)$$ are related by