Download Aug

95AM-4
Sr. No. 7
EXAMINATION OF MARINE ENGINEER OFFICER
Function: Marine Engineering at Operational Level
APPLIED MECHANICS
India (2003)
M.E.O. Class IV
(Time allowed - 3hours)
Morning Paper
Total Marks 100
NB : (1) All Questions are Compulsary
(2) All Questions carry equal marks
(3) Neatness in handwriting and clarity in expression carries weightage
(4) Illustration of an Answer with clear sketches / diagrams carries weightage.
1. A motor boat of 4 tonne displacement changes its velocity from 11 knots due North to 18 knots due
East in 30 seconds. Find the magnitude in m/s2 and direction of the average acceleration, and also
the average accelerating force on the boat. 1 knot = 1.852 km/h.
2. Two inclined planes, of 60° and 20° respectively, are placed back to back with a frictionless pulley
at the common vertex. A body is placed on each plane and connected by a cord running parallel to
the planes, and passing over the pulley. The mass of the body on the 60° plane is 10 kg and the
coefficient of friction is 0.4. The mass of the body on the 20° plane is 7.5 kg. If the system is just on
the point of moving, find the coefficient of friction between the 7.5 kg mass and its plane.
3. A beam carries a uniformly distributed load of 8.8 X 104 N/m over the left half of its length and a
uniformly distributed load of 4.4 x 104 N/m over the remaining half. The length of the beam is 6 m
and it is simply supported at two points, one at the extreme left end and the other within the right halflength at such a position to make the two reactions equal. Calculate the position of the right hand
reaction and sketch the shearing force and bending moment diagrams inserting the principal values.
4. A steel tube is 5 mm thick, 30 mm bore and 12 m long. A solid steel bar 20 mm diameter, screwed at
both ends with a thread of one mm pitch, passes centrally through the bolt. The ends of the tube are
covered by washers and tightened by nuts screwed on the ends of the bar. If the modulus of elasticity
of both tube and bar is 210 GN/m2, calculate the stress in the tube and bar when the nuts are screwed
up until the compressive force in the tube is 12.5 kN. Calculate also the increase in stress in the tube
and the bar when one nut is held and the other further tightened by one complete turn.
5. The diameters of the large and small pulleys of the compound sheave in a set of differential pulley
blocks are 120 mm and 110 mm respectively. Calculate the velocity ratio, mechanical advantage and
efficiency when lifting a load of 2.4 kN if the effort required is 250 N. Find also how much effort is
expended in friction.
6. Water escapes through a hole 20 mm diameter in the side of a tank, the head of water above the hole
being 3 m. Taking the coefficient of velocity as 0.97 and coefficient of reduction of area as 0.64,
calculate (I) the velocity of the water jet as it leaves the hole (II) the quantity of water escaping in
tonnes per hour.
7. A wire from a spring balance suspends a piece of brass and it registers a weight of 7 N in air. When
the brass is lowered into fresh water until submerged, the balance shows a weight of 6.17 N. Find the
specific gravity of this brass.
8. The torque to overcome frictional and other resistances of a turbine is 317 Nm and may be considered
as constant for all speeds. The mass of the rotating parts is 1.59 Mg and the radius of gyration is 686
mm. If the steam is cut off when the turbine is running free of load at 1920 rev/min, find the time it
will take to come to rest and the number of revolutions turned during that time.
9. The mass of the loaded carriage of a Fletcher’s Trolley apparatus is 5.44 kg and the mass of the load
on the hook at the hanging end of the cord is 0.22 kg. If friction is negligible, find the acceleration of
the carriage and the tension in the cord.
10. Find the width of a belt of 8 mm thickness required to drive a pulley 500 mm diameter at 450 rev/min
and transmit 4.5 kW of power, the maximum tension in the belt is not to exceed 7N per mm of width
and the tension in the tight side is to be taken as 2 ½ times the tension in the slack side.
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