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What do you mean by elastic bodies and plastic bodies?

Important Questions on Mechanical Properties of Solids

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Physics>Mechanical Properties of Matter>Mechanical Properties of Solids>Elastic Behaviour of Solids

A solid sphere of radius r made of a soft material of bulk modulus K is surrounded by a liquid in a cylindrical container. A massless piston of area

a

floats on the surface of the liquid, covering entire cross-section of cylindrical container. When a mass m is placed on the surface of the piston to compress the liquid, the fractional decrement in the radius of the sphere

(\frac{d r}{r})

, is:

MEDIUM

Physics>Mechanical Properties of Matter>Mechanical Properties of Solids>Elastic Behaviour of Solids

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

MEDIUM

Physics>Mechanical Properties of Matter>Mechanical Properties of Solids>Elastic Behaviour of Solids

The bulk modulus of a spherical object is

B

. If it is subjected to uniform pressure

p

, the fractional decrease in radius is

MEDIUM

Physics>Mechanical Properties of Matter>Mechanical Properties of Solids>Elastic Behaviour of Solids

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}

]

EASY

Physics>Mechanical Properties of Matter>Mechanical Properties of Solids>Elastic Behaviour of Solids

A constant force is applied to a metal wire of length

L

. Volume of the wire is constant. The extension produced is proportional to

HARD

Physics>Mechanical Properties of Matter>Mechanical Properties of Solids>Elastic Behaviour of Solids

A bottle has an opening of radius

a

and length

b

. A cork of length

b

and radius

(a + ∆ a)

where

(∆ a ≪ a)

, is compressed to fit into the opening completely (see figure). If the bulk modulus of cork is

B

and the coefficient of friction between the bottle and cork is

μ

, then the force needed to push the cork into the bottle is

Question Image

HARD

Physics>Mechanical Properties of Matter>Mechanical Properties of Solids>Elastic Behaviour of Solids

An external pressure

P

is applied on a cube at

0 ° C

so that it is equally compressed from all sides.

K

is the bulk modulus of the material of the cube and

α

is its coefficient of linear expansion. Suppose we want to bring the cube to its original size by heating. The temperature should be raised by:

MEDIUM

Physics>Mechanical Properties of Matter>Mechanical Properties of Solids>Elastic Behaviour of Solids

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>Elastic Behaviour of Solids

Two separate wires

A

and

B

are stretched by

2 mm

and

4 mm

respectively, when they are subjected to a force of

2 N .

Assume that both the wires are made up of same material and the radius of wire

B

4

times that of the radius of wire

A .

The length of the wires

A

and

B

are in the ratio of

a : b .

Then

\frac{a}{b}

can be expressed as

\frac{1}{x}

, where

x

is _____.

EASY

Physics>Mechanical Properties of Matter>Mechanical Properties of Solids>Elastic Behaviour of Solids

With rise in temperature, young's modulus of elasticity _________.

MEDIUM

Physics>Mechanical Properties of Matter>Mechanical Properties of Solids>Elastic Behaviour of Solids

A boy’s catapult is made of rubber cord which is

42 c m

long, with

6 m m

diameter of cross-section and of negligible mass. The boy keeps a stone weighing

0.02 k g

on it and stretches the cord by

20 c m

by applying a constant force. When released, the stone flies off with a velocity of

20 m s^{- 1}

. Neglect the change in the area of cross-section of the cord while stretched. The Young’s modulus of rubber is closest to:

MEDIUM

Physics>Mechanical Properties of Matter>Mechanical Properties of Solids>Elastic Behaviour of Solids

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:

EASY

Physics>Mechanical Properties of Matter>Mechanical Properties of Solids>Elastic Behaviour of Solids

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?

HARD

Physics>Mechanical Properties of Matter>Mechanical Properties of Solids>Elastic Behaviour of Solids

In plotting stress versus strain curves for two materials

P

and

Q

, a student by mistake puts strain on the

y

-axis and stress on the

x

- axis as shown in the figure. Then the correct statement(s) is(are)

Question Image

MEDIUM

Physics>Mechanical Properties of Matter>Mechanical Properties of Solids>Elastic Behaviour of Solids

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

MEDIUM

Physics>Mechanical Properties of Matter>Mechanical Properties of Solids>Elastic Behaviour of Solids

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

Physics>Mechanical Properties of Matter>Mechanical Properties of Solids>Elastic Behaviour of Solids

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

EASY

Physics>Mechanical Properties of Matter>Mechanical Properties of Solids>Elastic Behaviour of Solids

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>Elastic Behaviour of Solids

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}

]

EASY

Physics>Mechanical Properties of Matter>Mechanical Properties of Solids>Elastic Behaviour of Solids

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

What do you mean by elastic bodies and plastic bodies?

Important Questions on Mechanical Properties of Solids

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