Young's Modulus, Bulk Modulus and Modulus of Rigidity

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JEE Main 2019

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

5.0 mm

(C)

4.0 mm

(D)

3.0 mm

JEE Main 2021, 24 Feb Shift-II

LEVELJEE Main

A uniform metallic wire is elongated by $0.04 m$ when subjected to a linear force $F$ . The elongation, if its length and diameter is doubled and subjected to the same force will be ......... $cm$ .

JEE Main 2021, 31 Aug Shift-II

LEVELJEE Main

Four identical hollow cylindrical columns of mild steel support a big structure of mass $50 \times 1 0^{3}$ kg. The inner and outer radii of each column are $50$ cm and $100$ cm, respectively. Assuming, uniform local distribution, calculate the compression strain of each column. [Use, $Y = 2.0 \times 1 0^{11}$ Pa, $g = 9.8$ m/s $^{2}$ ].

(A)

3.60 \times 1 0^{- 8}

(B)

2.60 \times 1 0^{- 7}

(C)

1.87 \times 1 0^{- 3}

(D)

7.07 \times 1 0^{- 4}

JEE Main 2021, 31 Aug Shift-I

LEVELJEE Main

A uniform heavy rod of weight $10 kg ms^{- 2}$ , cross-sectional area $100 cm^{2}$ and length $20 cm$ is hanging from a fixed support. Young's modulus of the material of the rod is $2 \times 1 0^{11} Nm^{- 2}$ . Neglecting the lateral contraction, find the elongation of rod due to its own weight.

(A)

2 \times 1 0^{- 9} m

(B)

5 \times 1 0^{- 8} m

(C)

4 \times 1 0^{- 8} m

(D)

5 \times 1 0^{- 10} m

JEE Main 2021, 26 Feb Shift-II

LEVELJEE Main

The length of metallic wire is $l_{1}$ when tension in it is $T_{1}$ . It is $l_{2}$ when the tension is $T_{2}$ . The original length of the wire will be

(A)

\frac{l _{1} + l _{2}}{2}

(B)

\frac{T _{2} l _{1} + T _{1} l _{2}}{T _{1} + T _{2}}

(C)

\frac{T _{2} l _{1} - T _{1} l _{2}}{T _{2} - T _{1}}

(D)

\frac{T _{1} l _{1} - T _{2} l _{2}}{T _{2} - T _{1}}

JEE Main 2019, 8 April Shift-I

LEVELJEE Main

A steel wire having a radius of $2.0 mm$ , carrying a load of $4 kg$ , is hanging from a ceiling. Given that $g = 3.1 π ms^{- 2}$ , what will be the tensile stress that would be developed in the wire?

(A)

6.2 \times 1 0^{6} Nm^{- 2}

(B)

5.2 \times 1 0^{6} Nm^{- 2}

(C)

3.1 \times 1 0^{6} Nm^{- 2}

(D)

4.8 \times 1 0^{6} Nm^{- 2}

JEE Main 2021, 27 July Shift-I

LEVELJEE Main

A stone of mass $20 g$ is projected from a rubber catapult of length $0.1 m$ and area of cross-section $1 0^{- 6} m^{2}$ stretched by an amount $0.04 m$ . The velocity of the projected stone is ............ $m/s$ . (Take, Young's modulus of rubber $= 0.5 \times 1 0^{9} N/m^{2}$ )

JEE Main 2021, 31 Aug Shift-I

LEVELJEE Main

When a rubber ball is taken to a depth of ...... m in deep sea, its volume decreases by 0.5%. (The bulk modulus of rubber $= 9.8 \times 1 0^{8} Nm^{- 2}$ . Density of sea water $= 1 0^{3} kg m^{- 3}, g = 9.8 m/s^{2}$ )

JEE Main 2019, 10 April Shift-II

LEVELJEE Main

In an experiment, brass and steel wires of length 1 m each with areas of cross-section $1 mm^{2}$ 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 requires to produce a net elongation of 0.2 mm is [Take, the Young's modulus for steel and brass are respectively $120 \times 1 0^{9} N/m^{2}$ and $60 \times 1 0^{9} N/m^{2}$ ]

(A)

1.2 \times 1 0^{6} N/m^{2}

(B)

0.2 \times 1 0^{6} N/m^{2}

(C)

1.8 \times 1 0^{6} N/m^{2}

(D)

4.0 \times 1 0^{6} N/m^{2}

LEVELJEE Main

A wire fixed at the upper end stretches by length $l$ by applying a force $F$ . The work done in stretching is

(A)

\frac{F}{2 l}

(B)

F l

(C)

2 F l

(D)

\frac{F l}{2}

JEE Main 2020, 9 Jan Shift-II

LEVELJEE Main

Two steel wires having same length are suspended from a ceiling under the same load. If the ratio of their energy stored per unit volume is $1 : 4$ , the ratio of their diameters is

(A)

2 : 1

(B)

1 : 2

(C)

2 : 1

(D)

1 : 2

JEE Main 2021, 25 July Shift-I

LEVELJEE Main

Two wires of same length and radius are joined end-to-end and loaded. The Young's moduli of the materials of the two wires are $Y_{1}$ and $Y_{2}$ . The combination behaves as a single wire, then its Young's modulus is

(A)

Y = \frac{2 Y _{1} Y _{2}}{3 ( Y _{1} + Y _{2} )}

(B)

Y = \frac{2 Y _{1} Y _{2}}{Y _{1} + Y _{2}}

(C)

Y = \frac{Y _{1} Y _{2}}{2 ( Y _{1} + Y _{2} )}

(D)

Y = \frac{Y _{1} Y _{2}}{Y _{1} + Y _{2}}

JEE Main 2017 (Offline)

LEVELJEE Main

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

(A)

\frac{1}{9}

(B)

(C)

\frac{1}{81}

(D)

JEE Main 2021, 17 March Shift-II

LEVELJEE Main

An object is located at $2 km$ beneath the surface of the water. If the fractional compression $Δ V / V$ is $1.36%$ , the ratio of hydraulic stress to the corresponding hydraulic strain will be ............... . (Take, density of water is $1000 kg m^{- 3}$ and $g = 9.81 ms^{- 2}$ )

(A)

1.96 \times 1 0^{7} Nm^{- 2}

(B)

1.44 \times 1 0^{7} Nm^{- 2}

(C)

2.26 \times 1 0^{9} Nm^{- 2}

(D)

1.44 \times 1 0^{9} Nm^{- 2}

JEE Main 2020, 9 Jan Shift-I

LEVELJEE Main

A body of mass $m = 10 kg$ is attached to one end of a wire of length $0.3 m$ . The maximum angular speed (in $rad s^{- 1}$ ) with which it can be rotated about its other end in space station is (breaking stress of wire $= 4.8 \times 1 0^{7} Nm^{- 2}$ and area of cross-section of the wire $= 1 0^{- 2} cm^{2}$ ) is

LEVELJEE Main

If $S$ is stress and $Y$ is Young's modulus of material of a wire, the energy stored in the wire per unit volume is

(A)

2 S^{2} Y

(B)

\frac{S ^{2}}{2 Y}

(C)

\frac{2 Y}{S ^{2}}

(D)

\frac{S}{2 Y}

JEE Main 2018

LEVELJEE Main

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

(A)

\frac{K a}{m g}

(B)

\frac{K a}{3 m g}

(C)

\frac{m g}{3 K a}

(D)

\frac{m g}{K a}

JEE Main 2021, 27 Aug Shift-II

LEVELJEE Main

Wires $W_{1}$ and $W_{2}$ are made of same material having the breaking stress of $1.25 \times 1 0^{9} N/m^{2}$ . $W_{1}$ and $W_{2}$ have cross-sectional area of $8 \times 1 0^{- 7} m^{2}$ and $4 \times 1 0^{- 7} m^{2}$ , respectively. Masses of 20 kg and 10 kg hang from them as shown in the figure. The maximum mass that can be placed in the pan without breaking the wires is .......... kg. (Use, $g = 10 m/s^{2}$ )

JEE Main 2021, 18 March Shift-I

LEVELJEE Main

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 $B$ is $4$ times that of the radius of wire $A$ . The length of the wires $A$ and $B$ are in the ratio of $a : b$ . Then, $a / b$ can be expressed as $1/ x$ , where $x$ is ......... .

LEVELJEE Main

A wire suspended vertically from one of its ends is stretched by attaching a weight of $200 N$ to the lower end. The weight stretches the wire by $1 mm$ . Then, the elastic energy stored in the wire is

(A)

0.2 J

(B)

10 J

(C)

20 J

(D)

0.1 J

JEE Main 2019, 8 April Shift-I

LEVELJEE Main

A boy's catapult is made of rubber cord which is $42 cm$ long, with $6 mm$ diameter of cross-section and of negligible mass. The boy keeps a stone weighing $0.02 kg$ on it and stretches the cord by $20 cm$ by applying a constant force. When released the stone flies off with a velocity of $20 ms^{- 1}$ . Neglect the change in the area of cross-section of the cord while stretched. The Young's modulus of rubber is closest to

(A)

1 0^{6} Nm^{- 2}

(B)

1 0^{4} Nm^{- 2}

(C)

1 0^{8} Nm^{- 2}

(D)

1 0^{3} Nm^{- 2}

JEE Main 2021, 24 Feb Shift-I

LEVELJEE Main

If $Y, K$ and $η$ are the values of Young's modulus, bulk modulus and modulus of rigidity of any material, respectively. Choose the correct relation for these parameters.

(A)

Y = \frac{9 K η}{2 η + 3 K} N/m^{2}

(B)

Y = \frac{9 K η}{3 K - η} N/m^{2}

(C)

K = \frac{Y η}{9 η - 3 Y} N/m^{2}

(D)

η = \frac{3 Y K}{9 K + Y} N/m^{2}

JEE Main 2021, 20 July Shift-I

LEVELJEE Main

The value of tension in a long thin metal wire has been changed from $T_{1}$ to $T_{2}$ . The lengths of the metal wire at two different values of tension $T_{1}$ and $T_{2}$ are $l_{1}$ and $l_{2}$ , respectively. The actual length of the metal wire is

(A)

\frac{T _{2} l _{1} - T _{1} l _{2}}{T _{2} - T _{1}}

(B)

\frac{T _{1} l _{1} - T _{2} l _{2}}{T _{1} - T _{2}}

(C)

\frac{l _{1} + l _{2}}{2}

(D)

T_{1} T_{2} l_{1} l_{2}

JEE Main 2019, 8 April Shift-II

LEVELJEE Main

Young's moduli of two wires $A$ and $B$ are in the ratio $7 : 4$ . Wire $A$ is $2 m$ long and has radius $R$ . Wire $B$ is $1.5 m$ long and has radius $2 mm$ . If the two wires stretch by the same length for a given load, then the value of $R$ is close to

(A)

1.3 mm

(B)

1.5 mm

(C)

1.9 mm

(D)

1.7 mm

JEE Main 2019

LEVELJEE Main

The elastic limit of brass is $379 MPa$ . What should be the minimum diameter of a brass rod, if it is to support a $400 N$ load without exceeding its elastic limit?

(A)

0.90 mm

(B)

1.00 mm

(C)

1.16 mm

(D)

1.36 mm

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } The length of metallic wire is l1​ when tension in it is T1​. It is l2​ when the tension is T2​. The original length of the wire will be

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } A wire fixed at the upper end stretches by length l by applying a force F. The work done in stretching is

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

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } If S is stress and Y is Young's modulus of material of a wire, the energy stored in the wire per unit volume is

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } If Y,K and η are the values of Young's modulus, bulk modulus and modulus of rigidity of any material, respectively. Choose the correct relation for these parameters.

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } The elastic limit of brass is 379 MPa. What should be the minimum diameter of a brass rod, if it is to support a 400 N load without exceeding its elastic limit?

The length of metallic wire is $l_{1}$ when tension in it is $T_{1}$ . It is $l_{2}$ when the tension is $T_{2}$ . The original length of the wire will be

A wire fixed at the upper end stretches by length $l$ by applying a force $F$ . The work done in stretching is

If $S$ is stress and $Y$ is Young's modulus of material of a wire, the energy stored in the wire per unit volume is

If $Y, K$ and $η$ are the values of Young's modulus, bulk modulus and modulus of rigidity of any material, respectively. Choose the correct relation for these parameters.

The elastic limit of brass is $379 MPa$ . What should be the minimum diameter of a brass rod, if it is to support a $400 N$ load without exceeding its elastic limit?