PHYSICS PAPER - 1

PAPER WITH SOLUTION

PHYSICS PAPER - 1

PHYSICS [ JEE ADVANCED - 2019 ] PAPER - 1

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1.

Section -1 (Maximum Marks : 12)

This section contains Four (04) question.

Each question has Four option ONLY ONE of these four options is the correct answer.

Each question, choose the option corresponding to the correct answer.

Answer to each question will be evaluated according to the following marking scheme.

Full Marks : +3 If only Y the correct option is chosen.

Zero Marks : 0 If none of the option is chosen (i.e. the question is unanswered)

Negative Marks : ¨C1 in all other cases.

A current carrying wire heats a metal rod. The wire provides a constant power (P) to the rod. The

metal rod is enclosed in an insulated container. It is observed that the temperature (T) in the

metal rod changes with time (t) as

T(t) = T0(1 + ?t1/4)

where ? is a constant with appropriate dimension while T0 is a constant with dimension of of

temperature. The heat capacity of the metal is :

(1)

Ans.

4P(T(t) ¨C T0 )

? 4 T02

(2)

4P(T(t) ¨C T0 )2

?4 T03

(3)

4P(T(t) ¨C T0 )4

?4 T05

(4)

4P(T(t) ¨C T0 )3

?4 T04

4

dQ =HdT

dQ

dT

? H.

dt

dt

P = H. T0 . ????

1

. t¨C3/4

4

4P

? t¨C3/4.H

T0. ?

Now

T ¨C T0 = T0?t1/4

So

t

?

H?

3

2.

3/4

? T ¨C T0 ?

?

= ?

? T0? ?

4P(T ¨C T0 )3

T04?4

In a radioactive sample.

40

19

K nuclei either decay into stable

4.5¡Á10-10 per year or into stable

this sample all the stable

40

20

40

18

40

20

Ca nuclei with decay constant

Ar nuclei with decay constant 0.5¡Á10-10 per year. Given that in

Ca and

40

18

Ar nuclei are produced by the

t¡Á109 years. If the ratio of the sum of stable

40

20

Ca and

is 99. The value of t will be. [Given : In 10 = 2.3]

(1) 1.15

(2) 9.2

(3) 4.6

40

18

40

19

K nuclei only. In time

e

Ar nuclei to the radioactive

(4) 2.3

40

19

K nuclei

Sol.

2

Ca

0

Ar

0

K

t=0

dN

? ¨C(?1 ? ? 2 ) ? N

dt

?N?

loge ? ? ? ¨C(? ? ? 2 )t

? N0 ?

?

?

N0

¨C10

2.3 ? log10 ?

? ? 5 ? 10 t

N

/

100

? 0

?

2.303 ? 2

?t

5 ? 10¨C10

2.303 ¡Á 0.4 ¡Á 1010 = t

t = 9.2 ¡Á 109 year

3.

Consider a spherical gaseous cloud of mass density ?(r) in a free space where r is the radial

distance from its center. The gaseous cloud is made of particles of equal mass m moving in

circular orbits about the common center with the same kinetic energy K. The force acting on the

particles is their mutual gravitational force. If ?(r) is constant with time. the particle number

density n(r) = ?(r)/m is : (G = universal gravitational constant)

(1)

Ans.

K

?r m2G

(2)

2

3

M

Sol.

v

r

m

GMm mv2

?

r2

r

2 ?1

2?

= r ? 2 mv ?

?

?

?

GMm 2K

?

r2

r

?

M?

2Kr

Gm

3K

?r 2m2G

(3)

K

2?r 2m2G

(4)

K

6?r2m2G

dM ?

?

4?r 2dr? ?

?

??

?

4.

2K

dr

Gm

?

2K

dr

Gm

K

2?Gmr 2

k

p

=

2?Gm2r 2

m

A thin spherical insulating shell of radius R caries a uniformly distributed charge such that the

potential at its surface is V0. A hole with a small area ?4?R2 (? ................
................

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