2018-10-01_Physics_For_You

(a) g

L













12 /

(b)^3

4

g^12

L













/

(c)^33

2

12

g

L













/

(d)^3

2

g^12

L









/

19. A solid sphere is rotating abouit a diameter at an
    angular velocity Z. If it cools so that its radius
    reduces to^1
    n

of its original value, its angular velocity

becomes

(a)

Z

n

(b)

Z

n^2

(c) nZ (d) n^2 Z

20. A cube of mass m and height H slides with a speed

v. It strikes the obstacle of height h=H

4

. e speed
of the CM of the cube just aer the collision is

H

m

v

h

(a)

5

6

v (b)

3

6

v (c)

5

4

v (d)

3

4

v

SOLUTIONS

1. (d) : xCM = 0

or

mx mx mx mx

mmmm

11 22 33 44

1234

0







or (2m)(–a) + 4m(a) + m(a) + m 4 (–a) = 0

or m 4 = 3m

Similarly yCM = 0

or (2m)(–a) + 4m(–a) + m(a)

+ m 4 (a)= 0 or m 4 = 5m

Since, value of m 4 are dierent

to satisfy by both xCM = 0 and

yCM = 0

Hence, it is not possible.

2. (d) : Iring = Ml^2

IDisc =

Ml^2

2

Isquare =

Ml() 2

6

2

=

2

3

Ml^2 (Using Ar axis theorem)

Ifour rods = 4

4

2

12 4

2

Ml()M()l 2



























=

4

12

Ml^2

+ Ml^2

= Ml

2

3

+ Ml^2 =^4

3

Ml^2.

Thus, Ifour rods has the largest moment of inertia.

2 m

m 4

4 m

y m

a

a

x

aa

3. (b) : Loss in PE = Mg l
   2

 sin











Gain in KE

=

1

2

Mv^2 +

1

2

IZ^2

For ring, I = MR^2 , Z = v

R

Ÿ

1

2

IZ^2 =

1

2

MR^2 ×

v

R

2

2 =

1

2

Mv^2

Hence gain in K.E. =^1

2

Mv^2 +^1

2

Mv^2 = Mv^2

Ÿ Mv^2 = Mg

l

2

sin q Ÿ v =

glsinT

2

.

4. (c) : e acceleration of disc rolling down on an
   inclined plane is given by,

aroll = g

I

MR

sinθ

1 + disc 2

= g

MR

MR

sin

/



1

(^22)
 2
Ÿ aroll =^2
3
g sin q
Also, aslide = g sinq
a
a
roll
slide

=

2

3

s =

1

2 1

()at^2

slide =

1

2 2

()at^2

roll^ Ÿ^ aslide × t 1

(^2) = a
roll × t 2
2
Ÿ t
t
2
2
1

2 =

a

a

slide

roll

=^3

2

5. (b) : vP = Zrc

Z

P

O

q

q/

q/

r

rc r

As is evident, rc = 2

2

rcos











Ÿ vp =  2 

2

 rcos









 =^2 cos 2

T(Zr)

= 2

2

cos

T

(vCM) Ÿ vP = 2

2

vcos

T

q

q

l/

q/2r

rc q/2r

MONTHLY TUNE UP CLASS XII ANSWER KEY

1. (b) 2. (b) 3. (c) 4. (b) 5. (d)


2. (a) 7. (b) 8. (a) 9. (c) 10. (a)


3. (b) 12. (b) 13. (b) 14. (a) 15. (b)


4. (c) 17. (a) 18. (a) 19. (b) 20. (a,c,d)


5. (a,b,d) 22. (a,b,c) 23. (a,c) 24. (30) 25. (8)


6. (3.2) 27. (d) 28. (a) 29. (c) 30. (b)