1. 746 watts,

4. a; = ^ + - — r — ( f ~ ^ )' ^"^^'■

6 ^

8^^^ ' ^^^ t^6
distance and time

reckoned from the position where the velocity was V. Terminal

velocity, | .

8. H.p. = 38190; time=127-6 hrs. ; resistance = 236 -24 tons'
weight;

coal =4353 tons. {Geographical miles are meant.)

9. 6-81 X 10-12 kgm.-weight. 10. 3762 sees.

11. Mass of sun : mass of earth = (390)» : (13)1

12. 11-2 lbs. per ton; 358-4 h.p.

13. 4400 ft.-lb.-sec. units per sec. ; 17600 ft.-poundals per sec.

14. 14015 -.g. 15- 7" • 16- *•

17. HfS^fi' ^^^- P®' ^^*'*

18. v/480/£r sees. ; ijlbgl2 radians per sec.

19. 96^7- cms. per sec. per sec.

20. If the mass M be suspended at an arm r, and the moment of
inertia

of the wheel and axle be J, the acceleration = -ir-s-H^. If a Mr^ + I

length I unwrap in time t, the friction couple is

Mrg - (^Mr +-^'^j^.

21. V— •

22. When the rod has turned through an angle d, the two amounts
are

\ vigl sin d and | mgl sin 6 respectively.

23. Let the added mass have a radins of gyration h, and let its
centre

of gravity be x below the knife-edge ; then the positions are
given

by ^< = >^ respectively. 25. (i) «.^; (") a-^-J^-

26. (i) a • -^ below the point of suspension ; (ii) — below.O

27. Becomes /^l^ times as long. 28. 52-88 cms.

29. 2.^^.

30. (i) Multiplied by 4v'2 ; (ii) divided by 2^2 ; (iii) doubled.

31. VW sec. 32. 2-8 X 10^ pounds' weight per sq. in.

33. 2-6 xlC^ dynes per sq. cm. 34. Halved.

35. s&. cm. 36. 0-1875 cm. 37. i^^i^ ? ergs per c. cm.

38. Torsional rigidity, about 2-23 x Wg dynes per sq. cm. ; simple

rigidity, 2/ir times as much.

39. Five per cent., if the errors in n and Y are in opposite
senses.

40. 22001:22010-7.

41. 0000474 gm.

42. cms., assuming that the liquid wets the tube.OQort

43. 2-88x108; f^^ cms.

44. 1-2 cm.

45. 296000 dynes per sq. cm. 46. 0-0809 cm.

47. 01764 poundal per ft. 48. ^ dynes per cm. 49. -^«

50. (76s + 10) ^ + 156000, where « is the density of mercury.

51. 125960 ergs. 52. ^ gm. weight per sq. cm. 53. yj^'^"^'

KA . "*" , where P' is the external pressure and P is a
normal

***• 0-2214P •atmosphere, both in dynes per sq. cm.

58. (a) 0-0192, 1-016 ; (6) 19-2, 1016 dynes per sq. cm.

60. (a) 1-152 X 10-' cm., better 1-662 x 10"' ; (6) 1-016 x
lO"', better

1-466 X 10-«.

61. 000077 cm.

62. 226 cms.

63. Let the pressure outside the tyre be one atmosphere, and let

the internal pressure be n atmospheres ; then the time taken is

about 863000 (w'' - 1) log^o ( g _ ^^ _ ^ ) seconds. If n = 2,
this is

infinite (as it should be); if n=3, the time is 2-75x10° sees.;

for n = 4, 3-30 xlO« sees.; for n = 10, 7-60x108; for n = 20,

15-05 X 0", When the internal pressure considerably exceeds
the

external (as was probably intended), a rougher calculation is

appropriate, and leads to the result 750000 n sees. It will be

noticed that at 20 atmospheres, this is practically correct.

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