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Dimensional formula for Strain is

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Important Questions on Mechanical Properties of Solids

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Physics>Mechanical Properties of Matter>Mechanical Properties of Solids>Stress and Strain

A string of a material of length

1 m,

cross-sectional area

0.2 {cm}^{2}

requires

2000 N

to extend it by

1 mm

. The same material is used to manufacture the legs of a robot of

50 cm

length and of cross-sectional area

0.5 {cm}^{2}

each. The mass of the robot is

50 kg

. When it jumps from a building of height

h

, it experiences a strain

0.05 .

The maximum height through which the robot can jump without breaking its legs is

(g = 10 m s^{- 2})

HARD

Physics>Mechanical Properties of Matter>Mechanical Properties of Solids>Stress and Strain

A mild steel wire of length $2 L$ and cross-sectional area $A$ is stretched, well with in the elastic limit, horizontally between two pillars as shown in figure. A mass $m$ is suspended from the mid-point of the wire. Strain in the wire is

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Physics>Mechanical Properties of Matter>Mechanical Properties of Solids>Stress and Strain

The speed of the water in a river is

V

near the surface. If the coefficient of viscosity of water is

η

and the depth of the river is

H

, then the shearing stress between the horizontal layers of water is

MEDIUM

Physics>Mechanical Properties of Matter>Mechanical Properties of Solids>Stress and Strain

Consider two wires of same material having their ratio of radii to be

2 : 1

. If these two wires are stretched by equal force, the ratio of stress produced in them is :

MEDIUM

Physics>Mechanical Properties of Matter>Mechanical Properties of Solids>Stress and Strain

In an experiment, brass and steel wires of length

1 m

each with areas of cross section

1 m m^{2}

are used. The wires are connected in series and one end of the combined wire is connected to a rigid support and other end is subjected to elongation. The stress required to produce a net elongation of

0.2 m m

is,
[Given, the Young's Modulus for steel and brass are, respectively,

120 \times 10^{9} N / m^{2}

and

60 \times 10^{9} N / m^{2}

]

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Physics>Mechanical Properties of Matter>Mechanical Properties of Solids>Stress and Strain

If a tensile force is suddenly removed from a wire then its temperature will

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Physics>Mechanical Properties of Matter>Mechanical Properties of Solids>Stress and Strain

A wire of length

1 m

and radius

2 mm

is vertically clamped. The lower end is twisted through an angle of

45 °

. The angle of shear is _____

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Physics>Mechanical Properties of Matter>Mechanical Properties of Solids>Stress and Strain

A body of mass

m = 10 k g

is attached to one end of a wire of length

0.3 m

. What is the maximum angular speed (in

r a d s^{- 1}

) with which it can be rotated about its other end in a space station without breaking the wire?
[Breaking stress of wire

(σ)

= 4.8 \times 10^{7} N m^{- 2}

and area of cross-section of the wire

= 10^{- 2} c m^{2}

]

HARD

Physics>Mechanical Properties of Matter>Mechanical Properties of Solids>Stress and Strain

A lift is tied with thick iron ropes having mass

M

. The maximum acceleration of the lift is ‘

a m s^{- 2}

and maximum safe stress is

S N m^{- 2}

. The minimum diameter of the rope is

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Physics>Mechanical Properties of Matter>Mechanical Properties of Solids>Stress and Strain

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,

MEDIUM

Physics>Mechanical Properties of Matter>Mechanical Properties of Solids>Stress and Strain

The elastic limit of brass is

379 M P a

. The minimum diameter of a brass rod if it is to support a

400 N

load without exceeding its elastic limit will be

EASY

Physics>Mechanical Properties of Matter>Mechanical Properties of Solids>Stress and Strain

A cube of metal is subjected to a hydrostatic pressure

4 GPa

. The percentage change in the length of the side of the cube is close to : (Given bulk modulus of metal,

B = 8 \times 10^{10} Pa

)

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Physics>Mechanical Properties of Matter>Mechanical Properties of Solids>Stress and Strain

A particle of mass

1 kg

is moving in SHM with a path length of

0.01 m

and frequency of

50 Hz

. The maximum force in newton, acting on the particle is

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Physics>Mechanical Properties of Matter>Mechanical Properties of Solids>Stress and Strain

Two wires

A

and

B

are stretched by the same load. If the area of cross-section of wire '

A

' is double that of

^{'} B^{'}

, then the stress on '

B

' is

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Physics>Mechanical Properties of Matter>Mechanical Properties of Solids>Stress and Strain

One end of a horizontal thick copper wire of length

2 L

and radius

2 R

is welded to an end of another horizontal thin copper wire of length

L

and radius

R

. When the arrangement stretched by applying forces at two ends, the ratio of the elongation in the thin wire to that in the thick wire is

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Physics>Mechanical Properties of Matter>Mechanical Properties of Solids>Stress and Strain

A steel wire of cross-sectional area

4 {cm}^{2}

has elastic limit of

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

. The maximum upward acceleration that can be given to a

1000 kg

elevator supported by this steel wire if the stress is to exceed one-fourth of the elastic limit is [Take,

g = 10 m s^{- 2}

]

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Physics>Mechanical Properties of Matter>Mechanical Properties of Solids>Stress and Strain

Speed of a transverse wave on a straight wire (mass

6.0 g,

length

60 c m

and area of cross-section

1.0 m m^{2}

90 {m s}^{- 1}

. If the Young's modulus of wire is

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

, the extension of wire over its natural length is:

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Physics>Mechanical Properties of Matter>Mechanical Properties of Solids>Stress and Strain

A

and

B

are two wires. The radius of

A

is twice that of

B

. They are stretched by the same load. Then the stress on

B

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Physics>Mechanical Properties of Matter>Mechanical Properties of Solids>Stress and Strain

A man grows into a giant such that his linear dimensions increase by a factor of

9 .

Assuming that his density remains same, the stress in the leg will change by a factor of:

EASY

Physics>Mechanical Properties of Matter>Mechanical Properties of Solids>Stress and Strain

A steel wire having a radius of

2.0 m m

, carrying a load of

4 k g,

is hanging from a ceiling. Given that

g = 3.1 π m s^{- 2},

what will be the tensile stress that would be developed in the wire?

Dimensional formula for Strain is

Important Questions on Mechanical Properties of Solids

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