EASY

Earn 100

Explain the Poissons ratio and mention its limit

Important Questions on Elasticity

MEDIUM

Physics>Mechanical Properties of Matter>Elasticity>Hooke's Law and Elastic Modulus

Young's moduli of two wires

A

and

B

are in the ratio

7 : 4

. Wire

A

2 m

long and has radius

R .

Wire

B

1.5 m

long and has radius

2 m m .

If the two wires stretch by the same length for a given load, the value of

R

is close to:

HARD

Physics>Mechanical Properties of Matter>Elasticity>Hooke's Law and Elastic Modulus

A uniformly tapering conical wire is made from a material of Young's modulus

Y

and has a normal, unextended length

L

. The radii, at the upper and lower ends of this conical wire, have values

R

and

3 R

, respectively. The upper end of the wire is fixed to a rigid support and a mass

M

is suspended from its lower end. The equilibrium extended length, of this wire, would equal:

HARD

Physics>Mechanical Properties of Matter>Elasticity>Hooke's Law and Elastic Modulus

A thin

1 m

long rod has a radius of

5 mm

. A force of

50 {π×10}^{3} N

is applied at one end to determine its Young's modulus. Assume that the force is exactly known. If the least count in the measurement of all lengths is

0.01 mm

, which of the following statements is false?

EASY

Physics>Mechanical Properties of Matter>Elasticity>Hooke's Law and Elastic Modulus

An object of mass

m

is suspended at the end of a massless wire of length

L

and area of cross-section, A. Young modulus of the material of the wire is

Y

. If the mass is pulled down slightly its frequency of oscillation along the vertical direction is :

MEDIUM

Physics>Mechanical Properties of Matter>Elasticity>Hooke's Law and Elastic Modulus

A steel rail of length

5 m

and area of cross section

40 {cm}^{2}

is prevented from expanding along its length while the temperature rises by

10 ° C

. If coefficient of linear expansion and Young's modulus of steel are

1.2 \times 10^{- 5} K^{- 1}

and

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

respectively, the force developed in the rail is approximately:

EASY

Physics>Mechanical Properties of Matter>Elasticity>Hooke's Law and Elastic Modulus

A metallic rod breaks when strain produced is

0.2 %

. Young's modulus of the material of the rod is

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

. What should be its area of cross-section to support a load of

10^{4} N

HARD

Physics>Mechanical Properties of Matter>Elasticity>Hooke's Law and Elastic Modulus

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

MEDIUM

Physics>Mechanical Properties of Matter>Elasticity>Hooke's Law and Elastic Modulus

What is the pressure required to reduce the given volume of water by

1 %

? (Bulk modulus

(K) = 2 \times 10^{8} N m^{- 2}

)

HARD

Physics>Mechanical Properties of Matter>Elasticity>Hooke's Law and Elastic Modulus

A pendulum made of a uniform wire of cross sectional area A has time period T. When an additional mass M is added to its bob, the time period changes to

T_{M}

. If the Young's modulus of the material of the wire is

Y

, then

\frac{1}{Y}

is equal to:
(

g =

gravitational acceleration)

MEDIUM

Physics>Mechanical Properties of Matter>Elasticity>Hooke's Law and Elastic Modulus

The bulk modulus of a spherical object is

B

. If it is subjected to uniform pressure

p

, the fractional decrease in radius is

EASY

Physics>Mechanical Properties of Matter>Elasticity>Hooke's Law and Elastic Modulus

A wire of length

L

, area of cross section

A

is hanging from a fixed support. The length of the wire changes to

L_{1}

when mass

M

is suspended from its free end. The expression for Young’s modulus is:

MEDIUM

Physics>Mechanical Properties of Matter>Elasticity>Hooke's Law and Elastic Modulus

The Young's modulus of steel is twice that of brass. Two wires of same length and of same area of cross-section, one of steel and another of brass are suspended from the same roof. If we want the lower ends of the wires to be at the same level, then the weights added to the steel and brass wires must be in the ratio of:

EASY

Physics>Mechanical Properties of Matter>Elasticity>Hooke's Law and Elastic Modulus

The Young's modulus of a perfectly rigid body is

EASY

Physics>Mechanical Properties of Matter>Elasticity>Hooke's Law and Elastic Modulus

Copper of fixed volume

V

is drawn into wire of length

l

. When this wire is subjected to a constant force

F,

the extension produced in the wire is

∆ l .

Which of the following graph is a straight line?

MEDIUM

Physics>Mechanical Properties of Matter>Elasticity>Hooke's Law and Elastic Modulus

A rubber cord has a cross-sectional area

10^{- 6} m^{2}

and total unstretched length

0.1 m

. It is stretched to

0.125 m

and then released to project a particle of mass

5.0 g

. The velocity of projection is [Given, Young's modulus of rubber,

Y = 5 \times 10^{8} N m^{- 2}

]

HARD

Physics>Mechanical Properties of Matter>Elasticity>Hooke's Law and Elastic Modulus

String $A B$ of unstretched length $L$ is stretched by applying a force $F$ at the mid-point $C$ such that the segments $A C$ and $B C$ make an angle $θ$ with $A B$ as shown in the figure. The string may be considered as an elastic element with a force to elongation ratio $K$ . The force $F$ is given by

Question Image

EASY

Physics>Mechanical Properties of Matter>Elasticity>Hooke's Law and Elastic Modulus

The wrong statement in the following is

MEDIUM

Physics>Mechanical Properties of Matter>Elasticity>Hooke's Law and Elastic Modulus

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:

HARD

Physics>Mechanical Properties of Matter>Elasticity>Hooke's Law and Elastic Modulus

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>Elasticity>Hooke's Law and Elastic Modulus

A load of mass

M kg

is suspended from a steel wire of length

2 m

and radius

1.0 mm

in Searle's apparatus experiment. The increase in length produced in the wire is

4.0 mm .

Now the load is fully immersed in a liquid of relative density

2 .

The relative density of the material of load is

8 .

The new value of increase in length of the steel wire is:

Explain the Poissons ratio and mention its limit

Important Questions on Elasticity

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