Consider a slider crank mechanism with nonzero masses and inertia. A constant torque $$\tau $$ is applied on the crank as shown in the figure. Which of the following plots best resembles variation of crank angle, $$\theta $$ versus time

A circular solid disc of uniform thickness $$20mm,$$ radius $$200mm$$ and $$mass$$ $$20kg,$$ is used as a fly wheel. If it rotates at $$600$$ $$rpm,$$ the kinetic energy of the flywheel, in joules is

Which of the following statement is correct?

The torque (in N-m) exerted on the crank shaft of a two stroke engine can be described as is the crank angle as $$\,\,T = 10000 + 1000\sin 2\theta - 1200\,\cos 2\theta ,\,\,$$ where $$\,\theta \,\,$$ is the crank angle as measured from inner dead center position. Assuming the resisting torque to be constant, the power (in $$kW$$) developed by the engine at $$100$$ rpm is ________.

Torque and angular speed data over one cycle for a shaft carrying a flywheel are shown in the figures. The moment of inertia (in kg.m² ) of the flywheel is _______

Maximum fluctuation of kinetic energy in an engine has been calculated to be $$2600$$ J. Assuming that the engine runs at an average speed of $$200$$ rpm, the polar mass moment of inertia ( in kg.m² ) of a flywheel to keep the speed fluctuation within $$\, \pm 0.5\% $$ of the average speed is _______ .

Consider a flywheel whose mass $$M$$ is distributed almost equally between a heavy, ring-like rim of radius $$R$$ and a concentric disk-like feature of radius $$R/2$$. Other parts of the flywheel, such as spokes, etc, have negligible mass. The best approximation for $$\alpha ,$$ if the moment of inertia of the flywheel about its axis of rotation is expressed as $$\,\alpha M{R^2},\,\,$$ is ________.

A flywheel connected to a punching machine has to supply energy of $$400$$ Nm while running at a mean angular speed of $$20$$ rad/s. If the total fluctuation of speed is not to exceed $$ \pm 20\% $$, the mass moment of inertia of the flywheel in kg-m² is

The speed of an engine varies from $$210$$ rad/s to $$190$$ rad/s. During cycle the change in kinetic energy is found to be $$400$$ Nm. The inertia of the flywheel in kgm² is

If $${C_f}$$ is the coefficient of speed fluctuation of a flywheel then the ratio of $${\omega _{\max }}/{\omega _{\min }}$$ will be

For a certain engine having an average speed of $$1200$$ rpm, a flywheel approximated as a solid disc, is required for keeping the fluctuation of speed within $$2$$% about the average speed. The fluctuation of kinetic energy per cycle is found to be $$2$$kJ. What is the least possible mass of the flywheel if its diameter is not exceed $$1$$ m?

A flywheel of moment of inertia $$9.8$$ kg m² fluctuates by $$30$$ rpm for a fluctuation in energy of $$1936$$ Jouls. The mean speed of the flywheel is (in rpm)