Q: The length of an elastic string is a metre when the tension is 44 N, and b metre when the tension is 5 N. The length in metre when the tension is 9 N, is

As we know that,T1=K(l−l1)T2=K(l−l2)So, T2T1=(l−l2)l−l1∴T1l−T1l2=T2l−T2l1l=(T1−T2)T1l2−T2l1l=(5a−4b)…(i)k=b−a1…(ii)So, length of wire when tension is 9 N9=kl′(l′= change in length )9=(b−a)1×l′⇒l′=9b−9aHence, final length =l+l′=5a−4a+9a−9al0=5b−4a

Q: If Young's modulus of elasticity Y for a material is one and half times its rigidity coefficient η, the Poisson's ratio σ will be

Young's modulus, Y=23πWe know that Y=2n(1+σ)∴23n=2n(1+σ)⇒σ=−41

Q: x linear strain is produced in a wire of elasticity coefficient Y. The stored potential energy in unit volume of this wire is

Elastic potential energy per unit volume =21 stress × strain =21(Y× strain )× strain = 21Yx2

Question 1

The reason for the change in shape of a regular body is

Accepted Answer

Shearing strain causes change in shape of regular body.

Question 2

The Young's modulus of the material of a wire is equal to the

Accepted Answer

Young's modulus of material Y= Langitudinal strain  Linear stress ​ If longitudinal strain is equal unity, then Y= Linear stress produced

Question 3

To keep constant time, watches are fitted with balance wheel made of

Accepted Answer

Because dimension of invar does not vary with temperature

Question 4

The lower surface of a cube is fixed. On its upper surface, force is applied at an angle of 30∘ from its surface. The change will be of the type

Accepted Answer

There will be both shear stress and normal stress

Question 5

Which of the following affects the elasticity of a substance?

Accepted Answer

The elasticity of a substance is affected by Impurity of substance Hammering and annealing Change in temperature.

Question 6

The isothermal elasticity of a gas is equal to

Accepted Answer

Isothermal elasticity Ki​=P

Question 7

A stretched rubber has

Accepted Answer

A stretch rubber has increased potential energy

Question 8

The length of an elastic string is a metre when the tension is 44 N, and b metre when the tension is 5 N. The length in metre when the tension is 9 N, is

Accepted Answer

As we know that,T1​=K(l−l1​)T2​=K(l−l2​)So, T2​T1​​=(l−l2​)l−l1​​∴T1​l−T1​l2​=T2​l−T2​l1​l=(T1​−T2​)T1​l2​−T2​l1​​l=(5a−4b)…(i)k=b−a1​…(ii)So, length of wire when tension is 9 N9=kl′(l′= change in length )9=(b−a)1​×l′⇒l′=9b−9aHence, final length =l+l′=5a−4a+9a−9al0​=5b−4a

Question 9

The hollow shaft is _____ than a solid shaft of same mass, material and length.

Accepted Answer

A hollow shaft is more stiff than a solid of the same mass, material and length.

Question 10

If Young's modulus of elasticity Y for a material is one and half times its rigidity coefficient η, the Poisson's ratio σ will be

Accepted Answer

Young's modulus, Y=23π​We know that Y=2n(1+σ)​∴23n​=2n(1+σ)⇒σ=−41​​

Question 11

x linear strain is produced in a wire of elasticity coefficient Y. The stored potential energy in unit volume of this wire is

Accepted Answer

Elastic potential energy per unit volume =21​ stress × strain =21​(Y× strain )× strain = 21​Yx2

Question 12

The upper end of a wire of radius 4 mm length 100 cm is clamped and its other end is twisted through an angle of 30∘. Then angle of shear is

Accepted Answer

Asπθ=1ϕ;soϕ=1000.4×30∘​=0.12∘

Question 13

Coefficient of isothermal elasticity Eθ​ and coefficient of adiabatic elasticity Eϕ​ are related by (γ=Cp​/Cv​)

Accepted Answer

Adiabatic elasticity =γ× isothermal elastic
⇒Eϕ​=γEθ​

Question 14

Shearing stress causes change in

Accepted Answer

Shearing stress causes change in shape

Question 15

Which one of the following quantities does not have the unit of force per unit area?

Accepted Answer

Because strain is a dimensionless and unitless quantity

Question 16

The length of a wire is l1​ when the tension in it is 3 N and is l2​ when the tensions is 4 N. What will be its length when tension in it is 7 N ?

Accepted Answer

3=k(I1​−I0​)4=k(I2​−I0​)7=k(l1​+I2​−2I0​)

Question 17

If a man grows into a giant such that his linear dimensions increase by a factor of n1​. Assuming his density increases by a factor n2​, the stress in the leg will change by a factor of

Accepted Answer

V changes by n1​3F changes by n13​,n2​A changes by n1​2⇒ Stress changes by n1​n2​

Question 18

A horizontal aluminium  rod of diameter d projects length l from a wall. An object of mass m is suspended from the end of the rod. The shear modulus of aluminium is G. Neglecting the rod's mass the vertical deflection of the end of the rod will be

Accepted Answer

Shear strain =lx​G=πd2xmg4l​⇒x=πd2G4mgl​

Question 19

Equal torsional torques act on two rods x and y having equal length. The diameter of rod y is twice the diameter of rodx. If θx​ and θy​ are the angles of twist, then θy​θx​​=

Accepted Answer

Torsional torque is given asτx​=2lπηr4​θx​ and τy​=2lπη(2r)4​θy​Since, τx​=τy​∴θx​=16θy​ or θy​θx​​=16

Question 20

A tensile force of 2×103 N doubles the length of a rubber band of cross-sectional area 2×10−4 m2. The Young's modulus of elasticity of the rubber band is

Accepted Answer

Strain =lΔl​=ll​=1∴Y= stress =2×10−4 m22×103 N​=107Nm−2

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Solution for Class 11, Physics, Mechanical Properties of Solids

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