Applied Mechanics and Graphic Statics

21. A bullet weighing 10 gm moves with a velocity of l km/sec. Its kinetic energy is
(i) 5000 Nm
(ii) 5000 kg.m
(iii) 5000 J
The correct answer is

1. Only (ii)
2. Both (i) and (iii)
3. Both (ii) and (iii)
4. All (i), (ii) and (iii)

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22. A bullet weighing 200 g is fired horizontally with a velocity of 25 m/sec from a gun carried on a carriage which together with the gun weighs 100 kg. The velocity of recoil of the gun, will be

1. 0.01 m/sec
2. 0.05 m/sec
3. 1.00 m/sec
4. 1.5 m/see

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23. A cable loaded with 0.5 tonne per horizontal metre span is stretched between supports in the same horizontal line 400 m apart. If central dip is 20 m, the minimum tension in the cable, will be (A) 200 tonnes at the centre

1. 200 tonnes at the centre
2. 500 tonnes at the centre
3. 200 tonnes at the right support
4. 200 tonnes at the left support

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24. A cable loaded with 10 kN/m of span is stretched between supports in the same horizontal line 100 m apart. If the central dip is 10 m, then the maximum and minimum pull in the cable respectively are

1. 1346.3 kN and 1500 kN
2. 1436.2 kN and 1250 kN
3. 1346.3 kN and 1250 kN
4. 1436.2 kN and 1500 kN

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25. A car goes round a curve of radius 100 m at 25 m/sec. The angle to the horizontal at which the road must be banked to prevent sideways friction on the car wheels is tan"1 x, where x is (Assume g = 10 m/sec²)

1. 43680
2. 43497
3. 43594
4. 43682

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26. A circular disc rotates at n rpm. The angular velocity of a circular ring of same mass and radius as the disc and to have the same angular momentum is

1. n rpm
2. n/2 rpm
3. n/4 rpm
4. 2n rpm

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27. A cube on a smooth horizontal surface

1. Cannot be in stable equilibrium
2. Cannot be in neutral equilibrium
3. Cannot be in unstable equilibrium
4. Can be in any of these states

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28. A disc of mass 4 kg, radius 0.5 m and moment of inertia 3 kgm² rolls on a horizontal surface so that its center moves with speed 5 m/see. Kinetic energy of the disc is

1. 50 J
2. 150 J
3. 200 J
4. 400 J

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29. A flywheel of moment of inertia 20 kgm" is acted upon by a tangential force of 5 N at 2 m from its axis, for 3 seconds. The increase in angular velocity in radian per second is

1. 43497
2. 43499
3. 2
4. 3

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30. A force P of 50 N and another force Q of unknown magnitude act at 90° to each other. They are balanced by a force of 130 N. The magnitude of Q is

1. 60 N
2. 80 N
3. 100 N
4. 120 N

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