1. OBJECTIVE LEVEL I
1. (c) 2. (b)
3. (c) 4. (d)
5. (b) 6. (b)
7. (a) 8. (d)
9. (c) 10. (b)
11. (c) 12. (d)
13. (a) 14. (a)
15. (d)
OBJECTIVE LEVEL - II
1. (a) 2. (b)
3. (d) 4. (b)
5. (c) 6. (b)
7. (b) 8. (a)
9. (a) 10. (a)
11. (c) 12. (c)
13. (b) 14. (c)
15. (c)
(C.B.S.E.) SUBJECTIVE LEVEL - I
1. 6 cm. along OO from the sphere of smaller radius.
2.
2
(1 e)u sin2
g
 

2. 4. 5 m/sec.
5.
10
2 m/sec.
9
at 45º with x-axis.
6.
1
2
7.
100
3
metre
8. t = 155 second v = 2681 m/s.
9. mg
11. 18.29 m/sec2
.
13. momentum is conserved.
14. bob will not rise because whole momentum is transferred to the body at rest.
15. speed will remain constant.
SUBJECTIVE LEVEL - II
2. (i) rel
mu
m M

(ii)
ML
m M

3. (i)
2usin 1
g 1 e
  
 

 
(ii)
2
u sin 2
g(1 e)


(iii) 1 n
tan (e tan )

  
4. 2 1 3
m m m

5.
2
M
M m
l
 
 

 

3. 6. 3mv2
7. 0.167 N-s
8.
2 2
2
1 M mV
2 (m 2M)

9. 2
d
1 e

10. Vsphere
=
2
2
V(eM msin )
(M msin )
 
 
Vwedge
= 2
mvsin (1 e)
(M msin )
 
  .
SUBJECTIVE LEVEL - III
1.
2
Mv
h
2g(M m)


2.
2
max 2
M
h h
(m M)


3.
2
1 max
1 2
2m 2gr
V
m m


4. A
V 23.2 m /s
  40.3º
B
V 41.9 m/s
  55.6º
5.
Mx g
m 2H 2(H h)
 
 
 
,
Mx
m
left to the line of fall
6. (a)
m
M m
l l
 

(b)
mM dv
F
M m dt

 


4. 7.
12
x d
13

8.
2 2
2
2m gh cos
V
(M m)(M msin )


  
9. A
3
V u
4
 ; B
7
V u
4
 ;
3
J m
4
 u
10.  
A
1 ˆ ˆ
V i 7j
2
  

; B
1 ˆ ˆ
V ( i 9j)
4
  

.
PROBLEMS
1. 0
t 12s

v = 15.75 m/s
2. (a) 45º
  (b) v = 2 m/s
3. e = 0.84
M 15.12kg

4. (a) 0
5
v (6 gd)
2
  (b) x 6d 3
   .