1. A rigid triangular body, PQR, with sides of equal length of 1 unit moves on a flat plane. At the instant shown, edge QR is parallel to the x-axis, and the body moves such that velocities of points P and R are VP and VR , in the x and y directions, respectively. The magnitude of the angular velocity of the body is
2. A spur gear has pitch circle diameter D and number of teeth T. The circular pitch of the gear is
(A) πD / T
(B) T / D
(C) D / T
(D) 2πD / T
3. A slender uniform rigid bar of mass m is hinged at O and supported by two springs, with stiffnesses 3k and k, and a damper with damping coefficient c, as shown in the figure. For the system to be critically damped, the ratio c/√km should be
4. The crank of a slider-crank mechanism rotates counter-clockwise (CCW) with a constant angular velocity ω, as shown. Assume the length of the crank to be r.
Using exact analysis, the acceleration of the slider in the y-direction, at the instant shown, where the crank is parallel to x-axis, is given by
5. Two masses A and B having mass ma and mb, respectively, lying in the plane of the figure shown, are rigidly attached to a shaft which revolves about an axis through O perpendicular to the plane of the figure. The radii of rotation of the masses ma and mb are ra and rb, respectively. The angle between lines OA and OB is 90°. If ma = 10 kg, mb = 20 kg, ra = 200 mm and rb = 400 mm, then the balance mass to be placed at a radius of 200 mm is ______ kg (round off to two decimal places).
6. A four bar mechanism is shown in the figure. The link numbers are mentioned near the links. Input link 2 is rotating anticlockwise with a constant angular speed ω2. Length of different links are:
O2O4 = O2A = L
AB = O4B = √2L.
The magnitude of the angular speed of the output link 4 is ω4 at the instant when link 2 makes an angle of 90° with O2O4 as shown. The ratio ω4/ω2 is ______ (round off to two decimal places).
7. A uniform disc with radius r and a mass of m kg is mounted centrally on a horizontal axle of negligible mass and length of 1.5r. The disc spins counter-clockwise about the axle with angular speed ω, when viewed from the right-hand side bearing, Q. The axle precesses about a vertical axis at ωp = ω ⁄ 10 in the clockwise direction when viewed from above. Let RP and RQ (positive upwards) be the resultant reaction forces due to the mass and the gyroscopic effect, at bearings P and Q, respectively. Assuming ω2r = 300 m/s2 and g = 10 m/s2, the ratio of the larger to the smaller bearing reaction force (considering appropriate signs) is _______