An undamped spring-mass system with mass m and spring stiffness k is shown in the figure. The natural frequency and natural period of this system are $$\omega$$ rad/s and T s, respectively. If the stiffness of the spring is doubled and the mass is halved, then the natural frequency and the natural period of the modified system, respectively, are
A uniform rod KJ of weight w shown in the figure rests against a frictionless vertical wall at the point K and a rough horizontal surface at point J. It is given that w = 10 kN, a = 4 m and b = 3 m.
The minimum coefficient of static friction that is required at the point J to hold the rod in equilibrium is __________. (round off to three decimal places)
A 100 mg of HNO3 (strong acid) is added to water, bringing the final volume to 1.0 liter. Consider the atomic weights of H, N, and O, as 1 g/mol. 14 g mol. and 16 g/mol, respectively. The final pH of this water is (Ignore the dissociation of water.)
In a city, the chemical formula of biodegradable fraction of municipal solid waste (MSW) is C100H250O80N. The waste has to be treated by forced-aeration composting process for which air requirement has to be estimated.
Assume oxygen in air (by weight) = 23% and density of air = 1.3 kg/m3. Atomic mass : C = 12, H = 1, O = 16, N = 14.
C and H are oxidized completely whereas N is converted only into NH3 during oxidation.
For oxidative degradation of 1 tonne of the waste, the required theoretical volume of air (in m3/tonne) will be (round off the nearest integer)