A uniform disc of diameter 300 mm and of mass 5 kg is mounted on one end of an arm of length 600 mm. The other end of the arm is free to rotate in a universal bearing. If the disc rotates about the arm with a speed of 300 r.p.m. clockwise, looking from the front, with what speed will it precess about the vertical axis?

From the following data calculate the gyroscopic couple on the bearing in N-m. Mass of disc = 30 Kg, diameter = 60 cm Rotation speed = 1200 rpm Angle between disc and a plane 90 degree to the axis of shaft = 1°

A

180

B

186

C

190

D

196

A circular opening, 6m diameter, in a vertical side of a tank is closed by a disc of 6m diameter which can rotate about a horizontal diameter. Calculate the force on the disc. The centre of circular opening is at the depth of 5 m.

A

1.38 MN

B

2.76 MN

C

5.54 MN

D

7.85 MN

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

A

395

B

790

C

1580

D

3160

A disc is rotating with ω =10rad/s about a fixed central axis which is perpendicular to its plane. The disc has a mass =2kg & radius =10cm. A small particle of mass 100gm is put slowly on the disc’s outer circumference. There is sufficient friction between the disc and the particle. What will be the new angular velocity of the system?

A

10 rad/s

B

9.09 rad/s

C

9.51 rad/s

D

Can’t conserve angular momentum because of friction

Piston diameter = 0.24 m, length of stroke = 0.6 m, length of connecting rod = 1.5 m, mass of reciprocating parts = 300 kg, mass of connecting rod = 250 kg; speed of rotation = 125 r.p.m; centre of gravity of connecting rod from crank pin = 0.5 m ; Kg of the connecting rod about an axis through the centre of gravity = 0.65 m Find the equivalent length L of a simple pendulum swung about an axis.

A

1.35 m

B

1.42 m

C

1.48 m

D

1.50 m

A Pickering governor is driving a gramophone. Each disc attached to the centre of a leaf spring has a mass of 20 g. The width of each spring is 5 mm and thickness of 0.125 mm. The effective length of each spring is 40 mm. The distance from the spindle axis to the centre of gravity of the mass when the governor is at rest, is 10 mm, find the speed of the turntable in rpm if ratio of the governor speed to the turntable speed is 10.5.

A

25.5

B

2.43

C

51.0

D

12.25

For a porter governor, Each arm has a length of 250mm and pivoted on the axis of rotation. Sleeves carry a mass of 25kg and each ball’s mass is 5Kg. Radius of rotation: 150mm at the beginning of lift and 200mm at the maximum speed of governor. Find range in speed neglecting friction in rpm.

A

25

B

35

C

45

D

15

What is the monoisotopic and average mass of valine? Given data: Mass of the most abundant isotope of Carbon (C°)=12.0000, Mass of most abundant isotope of Hydrogen (H°)=1.0078, Mass of most abundant isotope of Oxygen (O°)=15.9949, Mass of most abundant isotope of Nitrogen (N°)=14.0031, The average mass of Carbon (C)=12.011, The average mass of Hydrogen (H)=1.008, The average mass of Oxygen (O)=15.999, The average mass of Nitrogen (N)=14.007.

A

99.068 and 99.2361

B

99.216 and 99.326

C

99.111 and 99.321

D

99.068 and 99.132

A rod of length L with uniform charge density $$\lambda $$ per unit length is in the XY-plane and rotating about Z-axis passing through one of its edge with an angularvelocity $$\overrightarrow \omega $$ as shown in the figure below. $$\left( {{\bf{\hat r}},\,\hat \phi ,\,{\bf{\hat z}}} \right)$$ refer to the unit vectors at Q, $$\overrightarrow {\bf{A}} $$ is the vector potential at a distance d from the origin O along Z-axis for d ≪ L and $$\overrightarrow {\bf{J}} $$ is the current density due to the motion of the rod. Which one of the following statements is correct?

A

$$\overrightarrow {\bf{J}} {\text{ along }}{\bf{\hat r}};\overrightarrow {\bf{A}} {\text{ along }}{\bf{\hat z}};\left| {\overrightarrow {\bf{A}} } \right| \propto \frac{1}{d}$$

B

$$\overrightarrow {\bf{J}} {\text{ along }}\hat \phi ;\overrightarrow {\bf{A}} {\text{ along }}\hat \phi ;\left| {\overrightarrow {\bf{A}} } \right| \propto \frac{1}{{{d^2}}}$$

C

$$\overrightarrow {\bf{J}} {\text{ along }}{\bf{\hat r}};\overrightarrow {\bf{A}} {\text{ along }}{\bf{\hat z}};\left| {\overrightarrow {\bf{A}} } \right| \propto \frac{1}{{{d^2}}}$$

D

$$\overrightarrow {\bf{J}} {\text{ along }}\hat \phi ;\overrightarrow {\bf{A}} {\text{ along }}\hat \phi ;\left| {\overrightarrow {\bf{A}} } \right| \propto \frac{1}{d}$$

The circumference of the back-sided wheel of a vehicle is 1 m greater than that of front side wheel. To travel 600 m, the front wheel rotates 30 times more than the back wheel. The circumference of the front wheel is :

A

2 m

B

4 m

C

5 m

D

None of these