An aeroplane makes a complete half circle of 50 metres radius, towards left, when flying at 200 km per hr. The rotary engine and the propeller of the plane has a mass of 400 kg and a radius of gyration of 0.3 m. The engine rotates at 2400 r.p.m. clockwise when viewed from the rear. Find the gyroscopic couple on the aircraft.

If the propeller of an aeroplane rotates clockwise when viewed from the rear and the aeroplane takes a right turn, the gyroscopic effect will

A

tend to raise the tail and depress the nose

B

tend to raise the nose and depress the tail

C

tilt the aeroplane about spin axis

D

have no effect

The engine of an aeroplane rotates in clockwise direction when seen from the tail end and the aeroplane takes a turn to the left. The effect of gyroscopic couple on the aeroplane will be

A

to dip the nose and tail

B

to raise the nose and tail

C

to raise the nose and dip of the tail

D

to dip the nose and raise the tail

The engine of an aeroplane rotates in clockwise direction when seen from the tail end and the aeroplane takes a turn to the left. The effect of the gyroscopic couple on the aeroplane will be

A

to raise the nose and dip the tail

B

to dip the nose and raise the tail

C

to raise the nose and tail

D

to dip the nose and tail

The engine of an aeroplane rotates in clockwise direction when seen from the tail end and the aeroplane takes a turn to the right. The effect of gyroscopic couple on the aeroplane will be to dip the nose and raise the tail.

A

True

B

False

A lady wants to buy the following items in the given price range- 1. Tomato between Rs. 40 and Rs. 45 per kg. 2. Grapes in the price range of Rs. 80 and Rs. 90 per kg. 3. Milk packets at Rs. 23 per liter. In which shop from the following will she definitely get all her items/ A. Shop S sells tomato at Rs. 22.5 per half kg, Grapes at Rs. 82 per kg and milk at Rs. 24 per liter. B. Shop H sells grapes at Rs. 21 per quarter kg, milk at 12.5 per half litre and tomato at Rs. 22 per half kg. C. Shop O sells milk at Rs. 11.5 per half litre, tomato at 21 per half kg and grapes at Rs. 43 per half kg. D. Shop P sells tomato at Rs. 23.5 per half kg, grapes at Rs. 85 per kg and milk at Rs. 23 per litre.

A

B

D

C

B

D

C

A ship propelled by a turbine rotor which has a mass of 5 tonnes and a speed of 2100 r.p.m. The rotor has a radius of gyration of 0.5 m and rotates in a clockwise direction when viewed from the stern. Find the gyroscopic effect when the ship sails at a speed of 30 km/h and steers to the left in a curve having 60 m radius.

A

38.5 kN-m

B

48.5 kN-m

C

58.5 kN-m

D

68.5 kN-m

The turbine rotor of a ship has a mass of 8 tonnes and a radius of gyration 0.6 m. It rotates at 1800 r.p.m. clockwise, when looking from the stern. Determine the gyroscopic couple, if the ship travels at 100 km/hr and steer to the left in a curve of 75 m radius.

A

100.866 kN-m

B

200.866 kN-m

C

300.866 kN-m

D

400.866 kN-m

A ship propelled by a turbine rotor which has a mass of 5 tonnes and a speed of 2100 r.p.m. The rotor has a radius of gyration of 0.5 m and rotates in a clockwise direction when viewed from the stern. Find the gyroscopic effect when the ship pitches 6 degree above and 6 degree below the horizontal position. The bow is descending with its maximum velocity. The motion due to pitching is simple harmonic and the periodic time is 20 seconds.

A

6075 N-m

B

7075 N-m

C

8075 N-m

D

9075 N-m

The heavy turbine rotor of a sea vessel rotates at 1500 r.p.m. clockwise looking from the stern, its mass being 750 kg. The vessel pitches with an angular velocity of 1 rad/s. Determine the gyroscopic couple transmitted to the hull when bow is rising, if the radius of gyration for the rotor is 250 mm.

A

4.364 kN-m

B

5.364 kN-m

C

6.364 kN-m

D

7.364 kN-m

The turbine rotor of a ship has a mass of 3500 kg. It has a radius of gyration of 0.45 m and a speed of 3000 r.p.m. clockwise when looking from stern. Determine the gyroscopic couple upon the ship when the ship is steering to the left on a curve of 100 m radius at a speed of 36 km/h.

A

11.27 kN-m

B

22.27 kN-m

C

33.27 kN-m

D

44.27 kN-m

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