The cross sections of two hollow bars made of the same material are concentric circles as shown in the figure. It is given that 𝑟₃ > 𝑟₁ and 𝑟₄ > 𝑟₂ , and that the areas of the cross-sections are the same. J₁ and J₂ are the torsional rigidities of the bars on the left and right, respectively. The ratioJ₂/J₁ is

A cantilever beam having square cross-section of side $$a$$ is subjected to an end load. If a is increases by $$19$$%, the tip deflection decreases approximately by

In the gear train shown, gear 3 is carried on arm 5. Gear 3 meshes with gear 2 and gear 4. The number of teeth on gear 2, 3, and 4 are 60, 20, and 100, respectively. If gear 2 is fixed and gear rotates with an angular velocity of 100 rpm in the counterclockwise direction, the angular speed of arm 5 (in rpm) is

A single degree of freedom spring mass system with viscous damping has a spring constant of 10 kN/m. The system is excited by a sinusoidal force of amplitude 100 N. If the damping factor (ratio) is 0.25, the amplitude of steady state oscillation at resonance is ________mm.