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In which type of diagram are the lengths of the bars proportional to the quantities they represent?

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Important Questions on Structure of Atom

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Chemistry>Physical Chemistry>Structure of Atom>Atomic Models

X = (4^{n} - 3 n - 1 : n \in N)

and

Y = \{9 (n - 1) : n \in N\}

, then

X \cap Y =

HARD

Chemistry>Physical Chemistry>Structure of Atom>Atomic Models

Let

Z

be the set of integers. If

A = \{x \in Z : 2^{(x + 2) (x^{2} - 5 x + 6)} = 1\}

and

B = {x \in Z : - 3 < 2 x - 1 < 9}

, then the number of subsets of the set

A \times B

, is :

EASY

Chemistry>Physical Chemistry>Structure of Atom>Atomic Models

Two finite sets have

m

and

n

elements. The number of subsets of the first set is

112

more than that of the second. The values of

m

and

n

are respectively

EASY

Chemistry>Physical Chemistry>Structure of Atom>Atomic Models

Let

S = \{1, 2, 3, \dots ., 100\}

, then number of non-empty subsets

A

S

such that the product of elements in

A

is even is :

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Chemistry>Physical Chemistry>Structure of Atom>Atomic Models

Let

A

and

B

be two sets containing

2

elements and

4

elements respectively. The number of subsets of

A \times B

having

3

or more elements is :

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Chemistry>Physical Chemistry>Structure of Atom>Atomic Models

The length of a metal wire is

l_{1}

when the tension in it is

T_{1}

and is

l_{2}

when the tension is

T_{2}

. The natural length of the wire is,

HARD

Chemistry>Physical Chemistry>Structure of Atom>Atomic Models

A mass

M

is hung at the free end of a wire suspended vertically from a rigid support. The wire has length

L

, area of cross-section

A

, linear mass density

μ

and Young's modulus

Y

. The extension produced in the wire is

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Chemistry>Physical Chemistry>Structure of Atom>Atomic Models

A glass slab is subjected to a pressure of

10

atm

. The fractional change in it's volume is: (Bulk modulus of glass =

37 \times 10^{9} N m^{- 2}, 1 a t m = 1 \times 10^{5} N m^{- 2}

)

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Chemistry>Physical Chemistry>Structure of Atom>Atomic Models

A metal wire of length

L_{1}

and area of cross-section

A

is attached to a rigid support. Another metal wire of Length

L_{2}

and of the same cross-section area is attached to the free end of the first wire. A body of mass

M

is then suspended from the free end of the second wire. If

Y_{1}

and

Y_{2}

are the Young’s moduli of the wires respectively, the effective force constant of the system of two wires is

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Chemistry>Physical Chemistry>Structure of Atom>Atomic Models

A stone of mass

m

is tied to one end of a wire of length

L

. The diameter of the wire is

D

and it is suspended vertically. The stone is now rotated in a horizontal plane and makes an angle

θ

with the vertical. If Young’s modulus of the wire is

Y

, then the increase in the length of the wire is

EASY

Chemistry>Physical Chemistry>Structure of Atom>Atomic Models

The adjacent graph shows the extension

(Δ l)

of a wire of length

l m

suspended from the top of a roof at one end and with a load

W

connected to the other end. If the cross-sectional area of the wire is

10^{- 6} m^{2}

, calculate the Young's modulus of the material of the wire -

Δ l (\times 10^{- 4} m)

EASY

Chemistry>Physical Chemistry>Structure of Atom>Atomic Models

Natural length of a spring is

60 cm

and its spring constant is

4000 N m^{- 1}

. A mass of

20 kg

is hung from it. The extension produced in the spring is (Take

g = 9.8 m s^{- 2}

)

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Chemistry>Physical Chemistry>Structure of Atom>Atomic Models

To what depth must a rubber ball be taken in the deep sea so that its volume is decrease by

0.1 %

.
(Take density of sea water =

10^{3} kg m^{- 3}

, bulk modulus of rubber =

9 \times 10^{8} N m^{- 2}

g = 10

m s^{- 2}

)

HARD

Chemistry>Physical Chemistry>Structure of Atom>Atomic Models

A wire of length

L

having area of cross-section

A

, linear mass density

μ

and the Young’s modulus

Y

is suspended vertically from a rigid support. The extension produced in the wire due to its own weight is:

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Chemistry>Physical Chemistry>Structure of Atom>Atomic Models

The compressibility of water is

6 \times 10^{- 10} N^{- 1} m^{2}

. If one litre is subjected to a pressure of

4 \times 10^{7} N m^{- 2}

, the decrease in its volume is

HARD

Chemistry>Physical Chemistry>Structure of Atom>Atomic Models

If the ratio of diameters, lengths and Young’s moduli of steel and brass wires shown in the figure are

p

q

and

r

respectively then, the corresponding ratio of increase in their lengths would be:
Question Image

EASY

Chemistry>Physical Chemistry>Structure of Atom>Atomic Models

A metal wire of length

l,

area of cross-section A and Young's modulus Y behaves as a spring of spring constant k given by

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Chemistry>Physical Chemistry>Structure of Atom>Atomic Models

A bar of length

l

, breadth

b

and depth

d

is supported at its ends and is loaded at the centre by a load

W

. If

Y

is the Young’s modulus of the material of the bar then, the depression

δ

at the centre is:

EASY

Chemistry>Physical Chemistry>Structure of Atom>Atomic Models

Which law deals with the study of variation of extension with applied force?

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Chemistry>Physical Chemistry>Structure of Atom>Atomic Models

One end of a nylon rope of length

4.5

m

and diameter

6

mm

is fixed to a free limb. A monkey weighing

100

N

jumps to catch the free end and stays there. The elongation of the rope is: (Given Young’s modulus of nylon =

4.8 \times 10^{11} N m^{- 2}

)

In which type of diagram are the lengths of the bars proportional to the quantities they represent?

Important Questions on Structure of Atom

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