A wheel of radius r rolls without slipping on a horizontal surface shown below. If the velocity of point P is 10m/s in the horizontal direction, the magnitude of velocity of point Q (in m/s) is ______

A pinion with radius $${r_1}$$, and inertia $${{\rm I}_1}$$ is driving a gear with radius $${r_2}$$ and inertia $${{\rm I}_2}$$ . Torque $${\tau _1}$$ is applied on pinion. The following are free body diagrams of pinion and gear showing important forces ($${F_1}$$and $${F_2}$$) of interaction. Which of the following relations hold true?

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 precision instrument package (m = 1kg) needs to be mounted on a surface vibrating at 60 Hz. It is desired that only 5% of the base surface vibration amplitude be transmitted to the instrument. Assume that the isolation is designed with its natural frequency significantly lesser than 60Hz, so that the effect of damping may be ignored. The stiffness (in N/m) of the required mounting pad is _____________.