HARD

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A uniform elastic wire of mass M and length L is hanging as shown in the figure. The Young’s modulus of elasticity of wire is Y and the area of cross section of the wire is A.

The elastic potential energy stored in the upper half is $\frac{a M^{b} g^{c} L}{48 A Y} .$ Find the value of a + b + c.

द्रव्यमान M तथा लम्बाई L के एक समरूप प्रत्यास्थ तार को चित्र में दर्शाये अनुसार लटकाया जाता है। तार का यंग प्रत्यास्थता गुणांक Y है तथा तार का अनुप्रस्थ काट क्षेत्रफल A है

ऊपरी आधे भाग में संग्रहित प्रत्यास्थ स्थितिज ऊर्जा $\frac{a M^{b} g^{c} L}{48 A Y}$ है। a + b + c का मान ज्ञात कीजिए।

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Important Questions on Properties of Solid and Liquid

EASY

Physics>Mechanics>Properties of Solid and Liquid>Hooke’s law

In materials like aluminium and copper, the correct order of magnitude of various elastic modulii is :

HARD

Physics>Mechanics>Properties of Solid and Liquid>Hooke’s law

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>Mechanics>Properties of Solid and Liquid>Hooke’s law

The bulk modulus of a spherical object is

B

. If it is subjected to uniform pressure

p

, the fractional decrease in radius is

HARD

Physics>Mechanics>Properties of Solid and Liquid>Hooke’s law

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

EASY

Physics>Mechanics>Properties of Solid and Liquid>Hooke’s law

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:

HARD

Physics>Mechanics>Properties of Solid and Liquid>Hooke’s law

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:

MEDIUM

Physics>Mechanics>Properties of Solid and Liquid>Hooke’s law

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:

MEDIUM

Physics>Mechanics>Properties of Solid and Liquid>Hooke’s law

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>Mechanics>Properties of Solid and Liquid>Hooke’s law

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>Mechanics>Properties of Solid and Liquid>Hooke’s law

A metal rod of length

L

and cross-sectional area

A

is heated through

T ° C

. What is the force required to prevent the expansion of the rod lengthwise?

[Y

= Young's modulus of the material of rod,

α =

coefficient of linear expansion

]

HARD

Physics>Mechanics>Properties of Solid and Liquid>Hooke’s law

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?

MEDIUM

Physics>Mechanics>Properties of Solid and Liquid>Hooke’s law

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>Mechanics>Properties of Solid and Liquid>Hooke’s law

When a block of mass

M

is suspended by a long wire of length

L

, the length of the wire becomes

(L + l) .

The elastic potential energy stored in the extended wire is

MEDIUM

Physics>Mechanics>Properties of Solid and Liquid>Hooke’s law

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:

EASY

Physics>Mechanics>Properties of Solid and Liquid>Hooke’s law

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?

EASY

Physics>Mechanics>Properties of Solid and Liquid>Hooke’s law

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>Mechanics>Properties of Solid and Liquid>Hooke’s law

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:

EASY

Physics>Mechanics>Properties of Solid and Liquid>Hooke’s law

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

MEDIUM

Physics>Mechanics>Properties of Solid and Liquid>Hooke’s law

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>Mechanics>Properties of Solid and Liquid>Hooke’s law

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:

Important Questions on Properties of Solid and Liquid

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