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PHXI09:MECHANICAL PROPERTIES OF SOLIDS

369818 The Young's modulus of brass and steel are respectively $1.0 \times 10^{11} N m^{- 2}$ and $2.0 \times 10^{11} N m^{- 2} .$ A brass wire and a steel wire of the same length are extended by $1 m m$ each under the same force. If radii of brass and steel wires are $R_{B}$ and $R_{S}$ respectively, then

1

R_{S} = \sqrt{2} R_{B}

2

R_{S} = \frac{R_{B}}{\sqrt{2}}

3

R_{S} = 4 R_{B}

4

R_{S} = \frac{R_{B}}{2}

Explanation:

Increase in length,
$Δ L = \frac{F L}{Y A} = \frac{F L}{Y π R^{2}}$
As $F, L$ and $Δ L$ are same, hence
$Y R^{2} = constant$
$∴ 2.0 \times 10^{11} R_{S}^{2} = 1.0 \times 10^{11} R_{B}^{2}$
$\Rightarrow R_{S} = \frac{R_{B}}{\sqrt{2}}$

PHXI09:MECHANICAL PROPERTIES OF SOLIDS

369819 A metal wire of length $L_{1}$ and area of cross section A is attached to a rigid support. Another metal wire of length $L_{2}$ and of the same cross sectional area is attached to the free end of the first wire. A body of mass $M$ is then suspended from the free end of the second wire. If $Y_{1}$ and $Y_{2}$ are the Young's moduli of the wires respectively, the effective force constant of the system of two wires is

1

[(Y_{1} Y_{2}) A] / {[(L_{1} L_{2})]}^{1 / 2}

2

[(Y_{1} Y_{2}) A] / [2 (Y_{1} L_{2} + Y_{2} L_{1})]

3

{(Y_{1} Y_{2})}^{1 / 2} A / {(L_{1} L_{2})}^{1 / 2}

4

[(Y_{1} Y_{2}) A] / (Y_{1} L_{2} + Y_{2} L_{1})

Explanation:

The force constant of a wire is $K = \frac{Y A}{l}$ for series combination
$k_{e} = \frac{k_{1} k_{2}}{k_{1} + k_{2}} = \frac{Y_{1} Y_{2} A}{Y_{1} L_{2} + Y_{2} L_{1}}$

PHXI09:MECHANICAL PROPERTIES OF SOLIDS

369820 The diameter of a brass rod is $4 m m$ and Young's modulus of brass is $9 \times 10^{10} N / m^{2}$ . The force required to stretch by $0.1 %$ of its length is:

1

36 N

2

360 π N

3

144 π \times 10^{3} N

4

36 π \times 10^{5} N

Explanation:

$L = 4 m$
$Y = 9 \times 10^{10}$
$\frac{F}{A} = Y \frac{Δ l}{l}$
$F = A Y \frac{Δ l}{l}$
$= π {(2 \times 10^{- 3})}^{2} \times 9 \times 10^{9} \times \frac{1}{100}$
$= π \times 4 \times 10^{- 6} \times 9 \times 10^{7}$
$= 360 π N .$

PHXI09:MECHANICAL PROPERTIES OF SOLIDS

369821 'Young's modulus' is defined as the ratio of

1 Bulk stress and longitudinal strain

2 Hydraulic stress and hydraulic strain

3 Shearing stress and shearing strain

4 Tensile stress and longitudinal strain

Explanation:

$Y = \frac{F / A}{\frac{Δ L}{L}} = \frac{Tensile stress}{Longitudinal strain}$

KCET - 2017

PHXI09:MECHANICAL PROPERTIES OF SOLIDS

369822 Two identical wires of substances ' $P$ ' and ' $Q$ ' are subjected to equal stretching force along the length. If the elongation of ' $Q$ ' is more than that of ' $P$ ', then

1 Both P and Q are equally elastic

2

P

is more elastic than

Q

3

P

is plastic and

Q

is elastic

4

Q

is more elastic than

P

Explanation:

Elasticity is the ability of a body to resist an external force causing deformation/ distortion. Given ' $Q$ ' is more elongated than $P$ when subjected to same stretching force, $P$ has more resisting strength than $Q$ , i.e., $P$ is more elastic than $Q$ .

PHXI09:MECHANICAL PROPERTIES OF SOLIDS

369818 The Young's modulus of brass and steel are respectively $1.0 \times 10^{11} N m^{- 2}$ and $2.0 \times 10^{11} N m^{- 2} .$ A brass wire and a steel wire of the same length are extended by $1 m m$ each under the same force. If radii of brass and steel wires are $R_{B}$ and $R_{S}$ respectively, then

1

R_{S} = \sqrt{2} R_{B}

2

R_{S} = \frac{R_{B}}{\sqrt{2}}

3

R_{S} = 4 R_{B}

4

R_{S} = \frac{R_{B}}{2}

Explanation:

Increase in length,
$Δ L = \frac{F L}{Y A} = \frac{F L}{Y π R^{2}}$
As $F, L$ and $Δ L$ are same, hence
$Y R^{2} = constant$
$∴ 2.0 \times 10^{11} R_{S}^{2} = 1.0 \times 10^{11} R_{B}^{2}$
$\Rightarrow R_{S} = \frac{R_{B}}{\sqrt{2}}$

PHXI09:MECHANICAL PROPERTIES OF SOLIDS

369819 A metal wire of length $L_{1}$ and area of cross section A is attached to a rigid support. Another metal wire of length $L_{2}$ and of the same cross sectional area is attached to the free end of the first wire. A body of mass $M$ is then suspended from the free end of the second wire. If $Y_{1}$ and $Y_{2}$ are the Young's moduli of the wires respectively, the effective force constant of the system of two wires is

1

[(Y_{1} Y_{2}) A] / {[(L_{1} L_{2})]}^{1 / 2}

2

[(Y_{1} Y_{2}) A] / [2 (Y_{1} L_{2} + Y_{2} L_{1})]

3

{(Y_{1} Y_{2})}^{1 / 2} A / {(L_{1} L_{2})}^{1 / 2}

4

[(Y_{1} Y_{2}) A] / (Y_{1} L_{2} + Y_{2} L_{1})

Explanation:

The force constant of a wire is $K = \frac{Y A}{l}$ for series combination
$k_{e} = \frac{k_{1} k_{2}}{k_{1} + k_{2}} = \frac{Y_{1} Y_{2} A}{Y_{1} L_{2} + Y_{2} L_{1}}$

PHXI09:MECHANICAL PROPERTIES OF SOLIDS

369820 The diameter of a brass rod is $4 m m$ and Young's modulus of brass is $9 \times 10^{10} N / m^{2}$ . The force required to stretch by $0.1 %$ of its length is:

1

36 N

2

360 π N

3

144 π \times 10^{3} N

4

36 π \times 10^{5} N

Explanation:

$L = 4 m$
$Y = 9 \times 10^{10}$
$\frac{F}{A} = Y \frac{Δ l}{l}$
$F = A Y \frac{Δ l}{l}$
$= π {(2 \times 10^{- 3})}^{2} \times 9 \times 10^{9} \times \frac{1}{100}$
$= π \times 4 \times 10^{- 6} \times 9 \times 10^{7}$
$= 360 π N .$

PHXI09:MECHANICAL PROPERTIES OF SOLIDS

369821 'Young's modulus' is defined as the ratio of

1 Bulk stress and longitudinal strain

2 Hydraulic stress and hydraulic strain

3 Shearing stress and shearing strain

4 Tensile stress and longitudinal strain

Explanation:

$Y = \frac{F / A}{\frac{Δ L}{L}} = \frac{Tensile stress}{Longitudinal strain}$

KCET - 2017

PHXI09:MECHANICAL PROPERTIES OF SOLIDS

369822 Two identical wires of substances ' $P$ ' and ' $Q$ ' are subjected to equal stretching force along the length. If the elongation of ' $Q$ ' is more than that of ' $P$ ', then

1 Both P and Q are equally elastic

2

P

is more elastic than

Q

3

P

is plastic and

Q

is elastic

4

Q

is more elastic than

P

Explanation:

Elasticity is the ability of a body to resist an external force causing deformation/ distortion. Given ' $Q$ ' is more elongated than $P$ when subjected to same stretching force, $P$ has more resisting strength than $Q$ , i.e., $P$ is more elastic than $Q$ .

PHXI09:MECHANICAL PROPERTIES OF SOLIDS

369818 The Young's modulus of brass and steel are respectively $1.0 \times 10^{11} N m^{- 2}$ and $2.0 \times 10^{11} N m^{- 2} .$ A brass wire and a steel wire of the same length are extended by $1 m m$ each under the same force. If radii of brass and steel wires are $R_{B}$ and $R_{S}$ respectively, then

1

R_{S} = \sqrt{2} R_{B}

2

R_{S} = \frac{R_{B}}{\sqrt{2}}

3

R_{S} = 4 R_{B}

4

R_{S} = \frac{R_{B}}{2}

Explanation:

Increase in length,
$Δ L = \frac{F L}{Y A} = \frac{F L}{Y π R^{2}}$
As $F, L$ and $Δ L$ are same, hence
$Y R^{2} = constant$
$∴ 2.0 \times 10^{11} R_{S}^{2} = 1.0 \times 10^{11} R_{B}^{2}$
$\Rightarrow R_{S} = \frac{R_{B}}{\sqrt{2}}$

PHXI09:MECHANICAL PROPERTIES OF SOLIDS

369819 A metal wire of length $L_{1}$ and area of cross section A is attached to a rigid support. Another metal wire of length $L_{2}$ and of the same cross sectional area is attached to the free end of the first wire. A body of mass $M$ is then suspended from the free end of the second wire. If $Y_{1}$ and $Y_{2}$ are the Young's moduli of the wires respectively, the effective force constant of the system of two wires is

1

[(Y_{1} Y_{2}) A] / {[(L_{1} L_{2})]}^{1 / 2}

2

[(Y_{1} Y_{2}) A] / [2 (Y_{1} L_{2} + Y_{2} L_{1})]

3

{(Y_{1} Y_{2})}^{1 / 2} A / {(L_{1} L_{2})}^{1 / 2}

4

[(Y_{1} Y_{2}) A] / (Y_{1} L_{2} + Y_{2} L_{1})

Explanation:

The force constant of a wire is $K = \frac{Y A}{l}$ for series combination
$k_{e} = \frac{k_{1} k_{2}}{k_{1} + k_{2}} = \frac{Y_{1} Y_{2} A}{Y_{1} L_{2} + Y_{2} L_{1}}$

PHXI09:MECHANICAL PROPERTIES OF SOLIDS

369820 The diameter of a brass rod is $4 m m$ and Young's modulus of brass is $9 \times 10^{10} N / m^{2}$ . The force required to stretch by $0.1 %$ of its length is:

1

36 N

2

360 π N

3

144 π \times 10^{3} N

4

36 π \times 10^{5} N

Explanation:

$L = 4 m$
$Y = 9 \times 10^{10}$
$\frac{F}{A} = Y \frac{Δ l}{l}$
$F = A Y \frac{Δ l}{l}$
$= π {(2 \times 10^{- 3})}^{2} \times 9 \times 10^{9} \times \frac{1}{100}$
$= π \times 4 \times 10^{- 6} \times 9 \times 10^{7}$
$= 360 π N .$

PHXI09:MECHANICAL PROPERTIES OF SOLIDS

369821 'Young's modulus' is defined as the ratio of

1 Bulk stress and longitudinal strain

2 Hydraulic stress and hydraulic strain

3 Shearing stress and shearing strain

4 Tensile stress and longitudinal strain

Explanation:

$Y = \frac{F / A}{\frac{Δ L}{L}} = \frac{Tensile stress}{Longitudinal strain}$

KCET - 2017

PHXI09:MECHANICAL PROPERTIES OF SOLIDS

369822 Two identical wires of substances ' $P$ ' and ' $Q$ ' are subjected to equal stretching force along the length. If the elongation of ' $Q$ ' is more than that of ' $P$ ', then

1 Both P and Q are equally elastic

2

P

is more elastic than

Q

3

P

is plastic and

Q

is elastic

4

Q

is more elastic than

P

Explanation:

Elasticity is the ability of a body to resist an external force causing deformation/ distortion. Given ' $Q$ ' is more elongated than $P$ when subjected to same stretching force, $P$ has more resisting strength than $Q$ , i.e., $P$ is more elastic than $Q$ .

PHXI09:MECHANICAL PROPERTIES OF SOLIDS

369818 The Young's modulus of brass and steel are respectively $1.0 \times 10^{11} N m^{- 2}$ and $2.0 \times 10^{11} N m^{- 2} .$ A brass wire and a steel wire of the same length are extended by $1 m m$ each under the same force. If radii of brass and steel wires are $R_{B}$ and $R_{S}$ respectively, then

1

R_{S} = \sqrt{2} R_{B}

2

R_{S} = \frac{R_{B}}{\sqrt{2}}

3

R_{S} = 4 R_{B}

4

R_{S} = \frac{R_{B}}{2}

Explanation:

Increase in length,
$Δ L = \frac{F L}{Y A} = \frac{F L}{Y π R^{2}}$
As $F, L$ and $Δ L$ are same, hence
$Y R^{2} = constant$
$∴ 2.0 \times 10^{11} R_{S}^{2} = 1.0 \times 10^{11} R_{B}^{2}$
$\Rightarrow R_{S} = \frac{R_{B}}{\sqrt{2}}$

PHXI09:MECHANICAL PROPERTIES OF SOLIDS

369819 A metal wire of length $L_{1}$ and area of cross section A is attached to a rigid support. Another metal wire of length $L_{2}$ and of the same cross sectional area is attached to the free end of the first wire. A body of mass $M$ is then suspended from the free end of the second wire. If $Y_{1}$ and $Y_{2}$ are the Young's moduli of the wires respectively, the effective force constant of the system of two wires is

1

[(Y_{1} Y_{2}) A] / {[(L_{1} L_{2})]}^{1 / 2}

2

[(Y_{1} Y_{2}) A] / [2 (Y_{1} L_{2} + Y_{2} L_{1})]

3

{(Y_{1} Y_{2})}^{1 / 2} A / {(L_{1} L_{2})}^{1 / 2}

4

[(Y_{1} Y_{2}) A] / (Y_{1} L_{2} + Y_{2} L_{1})

Explanation:

The force constant of a wire is $K = \frac{Y A}{l}$ for series combination
$k_{e} = \frac{k_{1} k_{2}}{k_{1} + k_{2}} = \frac{Y_{1} Y_{2} A}{Y_{1} L_{2} + Y_{2} L_{1}}$

PHXI09:MECHANICAL PROPERTIES OF SOLIDS

369820 The diameter of a brass rod is $4 m m$ and Young's modulus of brass is $9 \times 10^{10} N / m^{2}$ . The force required to stretch by $0.1 %$ of its length is:

1

36 N

2

360 π N

3

144 π \times 10^{3} N

4

36 π \times 10^{5} N

Explanation:

$L = 4 m$
$Y = 9 \times 10^{10}$
$\frac{F}{A} = Y \frac{Δ l}{l}$
$F = A Y \frac{Δ l}{l}$
$= π {(2 \times 10^{- 3})}^{2} \times 9 \times 10^{9} \times \frac{1}{100}$
$= π \times 4 \times 10^{- 6} \times 9 \times 10^{7}$
$= 360 π N .$

PHXI09:MECHANICAL PROPERTIES OF SOLIDS

369821 'Young's modulus' is defined as the ratio of

1 Bulk stress and longitudinal strain

2 Hydraulic stress and hydraulic strain

3 Shearing stress and shearing strain

4 Tensile stress and longitudinal strain

Explanation:

$Y = \frac{F / A}{\frac{Δ L}{L}} = \frac{Tensile stress}{Longitudinal strain}$

KCET - 2017

PHXI09:MECHANICAL PROPERTIES OF SOLIDS

369822 Two identical wires of substances ' $P$ ' and ' $Q$ ' are subjected to equal stretching force along the length. If the elongation of ' $Q$ ' is more than that of ' $P$ ', then

1 Both P and Q are equally elastic

2

P

is more elastic than

Q

3

P

is plastic and

Q

is elastic

4

Q

is more elastic than

P

Explanation:

Elasticity is the ability of a body to resist an external force causing deformation/ distortion. Given ' $Q$ ' is more elongated than $P$ when subjected to same stretching force, $P$ has more resisting strength than $Q$ , i.e., $P$ is more elastic than $Q$ .

PHXI09:MECHANICAL PROPERTIES OF SOLIDS

369818 The Young's modulus of brass and steel are respectively $1.0 \times 10^{11} N m^{- 2}$ and $2.0 \times 10^{11} N m^{- 2} .$ A brass wire and a steel wire of the same length are extended by $1 m m$ each under the same force. If radii of brass and steel wires are $R_{B}$ and $R_{S}$ respectively, then

1

R_{S} = \sqrt{2} R_{B}

2

R_{S} = \frac{R_{B}}{\sqrt{2}}

3

R_{S} = 4 R_{B}

4

R_{S} = \frac{R_{B}}{2}

Explanation:

Increase in length,
$Δ L = \frac{F L}{Y A} = \frac{F L}{Y π R^{2}}$
As $F, L$ and $Δ L$ are same, hence
$Y R^{2} = constant$
$∴ 2.0 \times 10^{11} R_{S}^{2} = 1.0 \times 10^{11} R_{B}^{2}$
$\Rightarrow R_{S} = \frac{R_{B}}{\sqrt{2}}$

PHXI09:MECHANICAL PROPERTIES OF SOLIDS

369819 A metal wire of length $L_{1}$ and area of cross section A is attached to a rigid support. Another metal wire of length $L_{2}$ and of the same cross sectional area is attached to the free end of the first wire. A body of mass $M$ is then suspended from the free end of the second wire. If $Y_{1}$ and $Y_{2}$ are the Young's moduli of the wires respectively, the effective force constant of the system of two wires is

1

[(Y_{1} Y_{2}) A] / {[(L_{1} L_{2})]}^{1 / 2}

2

[(Y_{1} Y_{2}) A] / [2 (Y_{1} L_{2} + Y_{2} L_{1})]

3

{(Y_{1} Y_{2})}^{1 / 2} A / {(L_{1} L_{2})}^{1 / 2}

4

[(Y_{1} Y_{2}) A] / (Y_{1} L_{2} + Y_{2} L_{1})

Explanation:

The force constant of a wire is $K = \frac{Y A}{l}$ for series combination
$k_{e} = \frac{k_{1} k_{2}}{k_{1} + k_{2}} = \frac{Y_{1} Y_{2} A}{Y_{1} L_{2} + Y_{2} L_{1}}$

PHXI09:MECHANICAL PROPERTIES OF SOLIDS

369820 The diameter of a brass rod is $4 m m$ and Young's modulus of brass is $9 \times 10^{10} N / m^{2}$ . The force required to stretch by $0.1 %$ of its length is:

1

36 N

2

360 π N

3

144 π \times 10^{3} N

4

36 π \times 10^{5} N

Explanation:

$L = 4 m$
$Y = 9 \times 10^{10}$
$\frac{F}{A} = Y \frac{Δ l}{l}$
$F = A Y \frac{Δ l}{l}$
$= π {(2 \times 10^{- 3})}^{2} \times 9 \times 10^{9} \times \frac{1}{100}$
$= π \times 4 \times 10^{- 6} \times 9 \times 10^{7}$
$= 360 π N .$

PHXI09:MECHANICAL PROPERTIES OF SOLIDS

369821 'Young's modulus' is defined as the ratio of

1 Bulk stress and longitudinal strain

2 Hydraulic stress and hydraulic strain

3 Shearing stress and shearing strain

4 Tensile stress and longitudinal strain

Explanation:

$Y = \frac{F / A}{\frac{Δ L}{L}} = \frac{Tensile stress}{Longitudinal strain}$

KCET - 2017

PHXI09:MECHANICAL PROPERTIES OF SOLIDS

369822 Two identical wires of substances ' $P$ ' and ' $Q$ ' are subjected to equal stretching force along the length. If the elongation of ' $Q$ ' is more than that of ' $P$ ', then

1 Both P and Q are equally elastic

2

P

is more elastic than

Q

3

P

is plastic and

Q

is elastic

4

Q

is more elastic than

P

Explanation:

Elasticity is the ability of a body to resist an external force causing deformation/ distortion. Given ' $Q$ ' is more elongated than $P$ when subjected to same stretching force, $P$ has more resisting strength than $Q$ , i.e., $P$ is more elastic than $Q$ .

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