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Page # 88
ROTATIONAL DYNAMICS
(JEE ADVANCED)
Exercise - III
1.
MR2
4R
–M
2
3
2
2.
14mr 2
5
3.
2r
6. w sin , when the bob is at the lowest point
mg
cot
2
8.
P=
10. (a)
3g
( cw )
4L
11.
2g
5
9.
(b) N
12. w =
100
15.
20. 48
21. gr/bh
25. M = 2m
2gh
R2
2
–1
3
N
Ml 2
2
7.
–14 i 10 j – 9k
5. 2mR2
3Ft 2
2m
13mg
,F
16
5 rad/s
14. 12 gm
4.
3 3
mg
16
3 3
16
13. at a distance a / 2 3 from the centre down the plane.
16. 13 W / 12
22.
(c)
mgl
8
26.16 kg m2/s
17.
R2 2
4g
23. 2
18. 2.1 rad/s2
24. (i) 10/13 m/s2, (ii) 5000/26 , (iii) 480/13 N
27. 2kkg m2 / s
28. 0.5 kg – m2 /s, 75 J
29. 19.7 rad/s
30. 60° east of south, 30° south of east. 31. (1/2)KE0
33. 120
34.
39.
v0
2v
( ), 0 (
3
3
)
7
mv2
10
40. (a)
Ft
m
35. 50m/s
(b)
19. 15
. 2 sec
36.
10gh
37.
7
6Ft
2F 2 t 2
F t
(c)
(d)
m
2
m
32.
10
g sin
7
41.
13
Mv2
16
3
38.
17
mg
7
42.
3
MR2
4
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