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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