140921
A steel wire can support a maximum load of $W$ before reaching its elastic limit. How much load can another wire, made out of identical steel, but with a radius one half the radius of the first wire, support before reaching its elastic limit?
1 $\mathrm{W}$
2 $\frac{\mathrm{W}}{2}$
3 $\frac{\mathrm{W}}{4}$
4 $4 \mathrm{~W}$
Explanation:
C Breaking stress $=\frac{\mathrm{W}}{\mathrm{A}}=\frac{\mathrm{W}}{\pi \mathrm{r}^{2}}$ For another steel wire, $\mathrm{r}^{\prime}=\frac{1}{2} \mathrm{r}, \mathrm{W}^{\prime}=?$ $\frac{\mathrm{W}^{\prime}}{\mathrm{A}^{\prime}}=\frac{4 \mathrm{~W}^{\prime}}{\pi \mathrm{r}^{2}}$ Since, Breaking stress is same for steel $\therefore \frac{4 \mathrm{~W}^{\prime}}{\pi \mathrm{r}^{2}}=\frac{\mathrm{W}}{\pi \mathrm{r}^{2}}$ $\Rightarrow \mathrm{W}^{\prime}=\frac{\mathrm{W}}{4}$
J and K-CET-2012
Mechanical Properties of Solids
140922
The stress-strain graph of a material is shown in the figure. The region in which the material is elastic is
1 $\mathrm{OA}$
2 $\mathrm{OB}$
3 $\mathrm{OC}$
4 $\mathrm{AC}$
Explanation:
A According to Hooke's law, stress is directly proportional to strain. Limit of Proportionality:- For point A:- It is a point where the linear nature of the stress-strain graph cases. For point B:- It is the limiting point for the condition that material behaves elastically, but Hooke's law does not apply. For point C:- Upper limit, Hooke's law does not apply.
J and K-CET-2016
Mechanical Properties of Solids
140924
A mass of $1 \mathrm{~kg}$ is suspended by means of a thread. The system is (i) lifted up with an acceleration of $4.9 \mathrm{~ms}^{-2}$ (ii) lowered with an acceleration of $4.9 \mathrm{~ms}^{-2}$. The ratio of tension in the first and second case is
1 $3: 1$
2 $1: 2$
3 $1: 3$
4 $2: 1$
Explanation:
A Given, $\mathrm{m}=1 \mathrm{~kg}, \mathrm{a}=4.9 \mathrm{~m} / \mathrm{s}^{2}$ (i) Tension in string $T_{1}=m g+m a$ up $=9.8 \mathrm{~N}+4.9 \mathrm{~N}$ $=14.7 \mathrm{~N}$ (ii) Tension in string $\mathrm{T}_{2}=\mathrm{mg}-\mathrm{ma}$ $\{\because$ Lift is moving down $\}$ $=9.8 \mathrm{~N}-4.9 \mathrm{~N}$ $=4.9 \mathrm{~N} $Ratio of the two tensions $\left(\frac{\mathrm{T}_{1}}{\mathrm{~T}_{2}}\right)=\frac{14.7 \mathrm{~N}}{4.9 \mathrm{~N}}$ $\frac{\mathrm{T}_{1}}{\mathrm{~T}_{2}}=3$ $\mathrm{T}_{1}: \mathrm{T}_{2}=3: 1$
WB JEE 2016
Mechanical Properties of Solids
140926
Which of the following substance has the highest elasticity?
1 Steel
2 Copper
3 Rubber
4 Sponge
Explanation:
A Modulus of elasticity (E) defined the value of elasticity, greater the value of $\mathrm{E}$ greater will be elasticity. Glass : 50 - $90 \mathrm{GPa}$ Rubber: $0.01-0.1 \mathrm{GPa}$ Steel : $210 \mathrm{GPa}$ Copper: $117 \mathrm{GPa}$ So, highest elasticity have steel.
WB JEE 2008
Mechanical Properties of Solids
140927
Which of the following statements is correct?
1 Hooke's law is applicable only within elastic limit
2 The adiabatic and isothermal elastic constants of a gas are equal
3 Young's modulus is dimensionless
4 Stress multiplied by strain is equal to the stored energy
Explanation:
A By Hooke's law, $\text { Elastic modulus }=\frac{\text { Stress }}{\text { Strain }}$ Hooke's law only works up to a certain limit after which the stress-strain graph does not follow the general pattern. The limit till which the Hooke's law is valid is known as elastic limit. So, statement (a) Hooke's law is applicable only within the elastic limit is correct. Let us consider option (b), The adiabatic constant of a gas is different from the isothermal elastic constant of a gas. So option (b) is incorrect. Let us consider option (c), Dimension of Young's modulus is $\mathrm{ML}^{-1} \mathrm{~T}^{-2}$. So option (c) is incorrect. Let us consider option (d) The half of stress multiplied by strain is elastic stored energy per unit volume. So, statement (d) is incorrect. Therefore, the correct option is (a).
140921
A steel wire can support a maximum load of $W$ before reaching its elastic limit. How much load can another wire, made out of identical steel, but with a radius one half the radius of the first wire, support before reaching its elastic limit?
1 $\mathrm{W}$
2 $\frac{\mathrm{W}}{2}$
3 $\frac{\mathrm{W}}{4}$
4 $4 \mathrm{~W}$
Explanation:
C Breaking stress $=\frac{\mathrm{W}}{\mathrm{A}}=\frac{\mathrm{W}}{\pi \mathrm{r}^{2}}$ For another steel wire, $\mathrm{r}^{\prime}=\frac{1}{2} \mathrm{r}, \mathrm{W}^{\prime}=?$ $\frac{\mathrm{W}^{\prime}}{\mathrm{A}^{\prime}}=\frac{4 \mathrm{~W}^{\prime}}{\pi \mathrm{r}^{2}}$ Since, Breaking stress is same for steel $\therefore \frac{4 \mathrm{~W}^{\prime}}{\pi \mathrm{r}^{2}}=\frac{\mathrm{W}}{\pi \mathrm{r}^{2}}$ $\Rightarrow \mathrm{W}^{\prime}=\frac{\mathrm{W}}{4}$
J and K-CET-2012
Mechanical Properties of Solids
140922
The stress-strain graph of a material is shown in the figure. The region in which the material is elastic is
1 $\mathrm{OA}$
2 $\mathrm{OB}$
3 $\mathrm{OC}$
4 $\mathrm{AC}$
Explanation:
A According to Hooke's law, stress is directly proportional to strain. Limit of Proportionality:- For point A:- It is a point where the linear nature of the stress-strain graph cases. For point B:- It is the limiting point for the condition that material behaves elastically, but Hooke's law does not apply. For point C:- Upper limit, Hooke's law does not apply.
J and K-CET-2016
Mechanical Properties of Solids
140924
A mass of $1 \mathrm{~kg}$ is suspended by means of a thread. The system is (i) lifted up with an acceleration of $4.9 \mathrm{~ms}^{-2}$ (ii) lowered with an acceleration of $4.9 \mathrm{~ms}^{-2}$. The ratio of tension in the first and second case is
1 $3: 1$
2 $1: 2$
3 $1: 3$
4 $2: 1$
Explanation:
A Given, $\mathrm{m}=1 \mathrm{~kg}, \mathrm{a}=4.9 \mathrm{~m} / \mathrm{s}^{2}$ (i) Tension in string $T_{1}=m g+m a$ up $=9.8 \mathrm{~N}+4.9 \mathrm{~N}$ $=14.7 \mathrm{~N}$ (ii) Tension in string $\mathrm{T}_{2}=\mathrm{mg}-\mathrm{ma}$ $\{\because$ Lift is moving down $\}$ $=9.8 \mathrm{~N}-4.9 \mathrm{~N}$ $=4.9 \mathrm{~N} $Ratio of the two tensions $\left(\frac{\mathrm{T}_{1}}{\mathrm{~T}_{2}}\right)=\frac{14.7 \mathrm{~N}}{4.9 \mathrm{~N}}$ $\frac{\mathrm{T}_{1}}{\mathrm{~T}_{2}}=3$ $\mathrm{T}_{1}: \mathrm{T}_{2}=3: 1$
WB JEE 2016
Mechanical Properties of Solids
140926
Which of the following substance has the highest elasticity?
1 Steel
2 Copper
3 Rubber
4 Sponge
Explanation:
A Modulus of elasticity (E) defined the value of elasticity, greater the value of $\mathrm{E}$ greater will be elasticity. Glass : 50 - $90 \mathrm{GPa}$ Rubber: $0.01-0.1 \mathrm{GPa}$ Steel : $210 \mathrm{GPa}$ Copper: $117 \mathrm{GPa}$ So, highest elasticity have steel.
WB JEE 2008
Mechanical Properties of Solids
140927
Which of the following statements is correct?
1 Hooke's law is applicable only within elastic limit
2 The adiabatic and isothermal elastic constants of a gas are equal
3 Young's modulus is dimensionless
4 Stress multiplied by strain is equal to the stored energy
Explanation:
A By Hooke's law, $\text { Elastic modulus }=\frac{\text { Stress }}{\text { Strain }}$ Hooke's law only works up to a certain limit after which the stress-strain graph does not follow the general pattern. The limit till which the Hooke's law is valid is known as elastic limit. So, statement (a) Hooke's law is applicable only within the elastic limit is correct. Let us consider option (b), The adiabatic constant of a gas is different from the isothermal elastic constant of a gas. So option (b) is incorrect. Let us consider option (c), Dimension of Young's modulus is $\mathrm{ML}^{-1} \mathrm{~T}^{-2}$. So option (c) is incorrect. Let us consider option (d) The half of stress multiplied by strain is elastic stored energy per unit volume. So, statement (d) is incorrect. Therefore, the correct option is (a).
140921
A steel wire can support a maximum load of $W$ before reaching its elastic limit. How much load can another wire, made out of identical steel, but with a radius one half the radius of the first wire, support before reaching its elastic limit?
1 $\mathrm{W}$
2 $\frac{\mathrm{W}}{2}$
3 $\frac{\mathrm{W}}{4}$
4 $4 \mathrm{~W}$
Explanation:
C Breaking stress $=\frac{\mathrm{W}}{\mathrm{A}}=\frac{\mathrm{W}}{\pi \mathrm{r}^{2}}$ For another steel wire, $\mathrm{r}^{\prime}=\frac{1}{2} \mathrm{r}, \mathrm{W}^{\prime}=?$ $\frac{\mathrm{W}^{\prime}}{\mathrm{A}^{\prime}}=\frac{4 \mathrm{~W}^{\prime}}{\pi \mathrm{r}^{2}}$ Since, Breaking stress is same for steel $\therefore \frac{4 \mathrm{~W}^{\prime}}{\pi \mathrm{r}^{2}}=\frac{\mathrm{W}}{\pi \mathrm{r}^{2}}$ $\Rightarrow \mathrm{W}^{\prime}=\frac{\mathrm{W}}{4}$
J and K-CET-2012
Mechanical Properties of Solids
140922
The stress-strain graph of a material is shown in the figure. The region in which the material is elastic is
1 $\mathrm{OA}$
2 $\mathrm{OB}$
3 $\mathrm{OC}$
4 $\mathrm{AC}$
Explanation:
A According to Hooke's law, stress is directly proportional to strain. Limit of Proportionality:- For point A:- It is a point where the linear nature of the stress-strain graph cases. For point B:- It is the limiting point for the condition that material behaves elastically, but Hooke's law does not apply. For point C:- Upper limit, Hooke's law does not apply.
J and K-CET-2016
Mechanical Properties of Solids
140924
A mass of $1 \mathrm{~kg}$ is suspended by means of a thread. The system is (i) lifted up with an acceleration of $4.9 \mathrm{~ms}^{-2}$ (ii) lowered with an acceleration of $4.9 \mathrm{~ms}^{-2}$. The ratio of tension in the first and second case is
1 $3: 1$
2 $1: 2$
3 $1: 3$
4 $2: 1$
Explanation:
A Given, $\mathrm{m}=1 \mathrm{~kg}, \mathrm{a}=4.9 \mathrm{~m} / \mathrm{s}^{2}$ (i) Tension in string $T_{1}=m g+m a$ up $=9.8 \mathrm{~N}+4.9 \mathrm{~N}$ $=14.7 \mathrm{~N}$ (ii) Tension in string $\mathrm{T}_{2}=\mathrm{mg}-\mathrm{ma}$ $\{\because$ Lift is moving down $\}$ $=9.8 \mathrm{~N}-4.9 \mathrm{~N}$ $=4.9 \mathrm{~N} $Ratio of the two tensions $\left(\frac{\mathrm{T}_{1}}{\mathrm{~T}_{2}}\right)=\frac{14.7 \mathrm{~N}}{4.9 \mathrm{~N}}$ $\frac{\mathrm{T}_{1}}{\mathrm{~T}_{2}}=3$ $\mathrm{T}_{1}: \mathrm{T}_{2}=3: 1$
WB JEE 2016
Mechanical Properties of Solids
140926
Which of the following substance has the highest elasticity?
1 Steel
2 Copper
3 Rubber
4 Sponge
Explanation:
A Modulus of elasticity (E) defined the value of elasticity, greater the value of $\mathrm{E}$ greater will be elasticity. Glass : 50 - $90 \mathrm{GPa}$ Rubber: $0.01-0.1 \mathrm{GPa}$ Steel : $210 \mathrm{GPa}$ Copper: $117 \mathrm{GPa}$ So, highest elasticity have steel.
WB JEE 2008
Mechanical Properties of Solids
140927
Which of the following statements is correct?
1 Hooke's law is applicable only within elastic limit
2 The adiabatic and isothermal elastic constants of a gas are equal
3 Young's modulus is dimensionless
4 Stress multiplied by strain is equal to the stored energy
Explanation:
A By Hooke's law, $\text { Elastic modulus }=\frac{\text { Stress }}{\text { Strain }}$ Hooke's law only works up to a certain limit after which the stress-strain graph does not follow the general pattern. The limit till which the Hooke's law is valid is known as elastic limit. So, statement (a) Hooke's law is applicable only within the elastic limit is correct. Let us consider option (b), The adiabatic constant of a gas is different from the isothermal elastic constant of a gas. So option (b) is incorrect. Let us consider option (c), Dimension of Young's modulus is $\mathrm{ML}^{-1} \mathrm{~T}^{-2}$. So option (c) is incorrect. Let us consider option (d) The half of stress multiplied by strain is elastic stored energy per unit volume. So, statement (d) is incorrect. Therefore, the correct option is (a).
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Mechanical Properties of Solids
140921
A steel wire can support a maximum load of $W$ before reaching its elastic limit. How much load can another wire, made out of identical steel, but with a radius one half the radius of the first wire, support before reaching its elastic limit?
1 $\mathrm{W}$
2 $\frac{\mathrm{W}}{2}$
3 $\frac{\mathrm{W}}{4}$
4 $4 \mathrm{~W}$
Explanation:
C Breaking stress $=\frac{\mathrm{W}}{\mathrm{A}}=\frac{\mathrm{W}}{\pi \mathrm{r}^{2}}$ For another steel wire, $\mathrm{r}^{\prime}=\frac{1}{2} \mathrm{r}, \mathrm{W}^{\prime}=?$ $\frac{\mathrm{W}^{\prime}}{\mathrm{A}^{\prime}}=\frac{4 \mathrm{~W}^{\prime}}{\pi \mathrm{r}^{2}}$ Since, Breaking stress is same for steel $\therefore \frac{4 \mathrm{~W}^{\prime}}{\pi \mathrm{r}^{2}}=\frac{\mathrm{W}}{\pi \mathrm{r}^{2}}$ $\Rightarrow \mathrm{W}^{\prime}=\frac{\mathrm{W}}{4}$
J and K-CET-2012
Mechanical Properties of Solids
140922
The stress-strain graph of a material is shown in the figure. The region in which the material is elastic is
1 $\mathrm{OA}$
2 $\mathrm{OB}$
3 $\mathrm{OC}$
4 $\mathrm{AC}$
Explanation:
A According to Hooke's law, stress is directly proportional to strain. Limit of Proportionality:- For point A:- It is a point where the linear nature of the stress-strain graph cases. For point B:- It is the limiting point for the condition that material behaves elastically, but Hooke's law does not apply. For point C:- Upper limit, Hooke's law does not apply.
J and K-CET-2016
Mechanical Properties of Solids
140924
A mass of $1 \mathrm{~kg}$ is suspended by means of a thread. The system is (i) lifted up with an acceleration of $4.9 \mathrm{~ms}^{-2}$ (ii) lowered with an acceleration of $4.9 \mathrm{~ms}^{-2}$. The ratio of tension in the first and second case is
1 $3: 1$
2 $1: 2$
3 $1: 3$
4 $2: 1$
Explanation:
A Given, $\mathrm{m}=1 \mathrm{~kg}, \mathrm{a}=4.9 \mathrm{~m} / \mathrm{s}^{2}$ (i) Tension in string $T_{1}=m g+m a$ up $=9.8 \mathrm{~N}+4.9 \mathrm{~N}$ $=14.7 \mathrm{~N}$ (ii) Tension in string $\mathrm{T}_{2}=\mathrm{mg}-\mathrm{ma}$ $\{\because$ Lift is moving down $\}$ $=9.8 \mathrm{~N}-4.9 \mathrm{~N}$ $=4.9 \mathrm{~N} $Ratio of the two tensions $\left(\frac{\mathrm{T}_{1}}{\mathrm{~T}_{2}}\right)=\frac{14.7 \mathrm{~N}}{4.9 \mathrm{~N}}$ $\frac{\mathrm{T}_{1}}{\mathrm{~T}_{2}}=3$ $\mathrm{T}_{1}: \mathrm{T}_{2}=3: 1$
WB JEE 2016
Mechanical Properties of Solids
140926
Which of the following substance has the highest elasticity?
1 Steel
2 Copper
3 Rubber
4 Sponge
Explanation:
A Modulus of elasticity (E) defined the value of elasticity, greater the value of $\mathrm{E}$ greater will be elasticity. Glass : 50 - $90 \mathrm{GPa}$ Rubber: $0.01-0.1 \mathrm{GPa}$ Steel : $210 \mathrm{GPa}$ Copper: $117 \mathrm{GPa}$ So, highest elasticity have steel.
WB JEE 2008
Mechanical Properties of Solids
140927
Which of the following statements is correct?
1 Hooke's law is applicable only within elastic limit
2 The adiabatic and isothermal elastic constants of a gas are equal
3 Young's modulus is dimensionless
4 Stress multiplied by strain is equal to the stored energy
Explanation:
A By Hooke's law, $\text { Elastic modulus }=\frac{\text { Stress }}{\text { Strain }}$ Hooke's law only works up to a certain limit after which the stress-strain graph does not follow the general pattern. The limit till which the Hooke's law is valid is known as elastic limit. So, statement (a) Hooke's law is applicable only within the elastic limit is correct. Let us consider option (b), The adiabatic constant of a gas is different from the isothermal elastic constant of a gas. So option (b) is incorrect. Let us consider option (c), Dimension of Young's modulus is $\mathrm{ML}^{-1} \mathrm{~T}^{-2}$. So option (c) is incorrect. Let us consider option (d) The half of stress multiplied by strain is elastic stored energy per unit volume. So, statement (d) is incorrect. Therefore, the correct option is (a).
140921
A steel wire can support a maximum load of $W$ before reaching its elastic limit. How much load can another wire, made out of identical steel, but with a radius one half the radius of the first wire, support before reaching its elastic limit?
1 $\mathrm{W}$
2 $\frac{\mathrm{W}}{2}$
3 $\frac{\mathrm{W}}{4}$
4 $4 \mathrm{~W}$
Explanation:
C Breaking stress $=\frac{\mathrm{W}}{\mathrm{A}}=\frac{\mathrm{W}}{\pi \mathrm{r}^{2}}$ For another steel wire, $\mathrm{r}^{\prime}=\frac{1}{2} \mathrm{r}, \mathrm{W}^{\prime}=?$ $\frac{\mathrm{W}^{\prime}}{\mathrm{A}^{\prime}}=\frac{4 \mathrm{~W}^{\prime}}{\pi \mathrm{r}^{2}}$ Since, Breaking stress is same for steel $\therefore \frac{4 \mathrm{~W}^{\prime}}{\pi \mathrm{r}^{2}}=\frac{\mathrm{W}}{\pi \mathrm{r}^{2}}$ $\Rightarrow \mathrm{W}^{\prime}=\frac{\mathrm{W}}{4}$
J and K-CET-2012
Mechanical Properties of Solids
140922
The stress-strain graph of a material is shown in the figure. The region in which the material is elastic is
1 $\mathrm{OA}$
2 $\mathrm{OB}$
3 $\mathrm{OC}$
4 $\mathrm{AC}$
Explanation:
A According to Hooke's law, stress is directly proportional to strain. Limit of Proportionality:- For point A:- It is a point where the linear nature of the stress-strain graph cases. For point B:- It is the limiting point for the condition that material behaves elastically, but Hooke's law does not apply. For point C:- Upper limit, Hooke's law does not apply.
J and K-CET-2016
Mechanical Properties of Solids
140924
A mass of $1 \mathrm{~kg}$ is suspended by means of a thread. The system is (i) lifted up with an acceleration of $4.9 \mathrm{~ms}^{-2}$ (ii) lowered with an acceleration of $4.9 \mathrm{~ms}^{-2}$. The ratio of tension in the first and second case is
1 $3: 1$
2 $1: 2$
3 $1: 3$
4 $2: 1$
Explanation:
A Given, $\mathrm{m}=1 \mathrm{~kg}, \mathrm{a}=4.9 \mathrm{~m} / \mathrm{s}^{2}$ (i) Tension in string $T_{1}=m g+m a$ up $=9.8 \mathrm{~N}+4.9 \mathrm{~N}$ $=14.7 \mathrm{~N}$ (ii) Tension in string $\mathrm{T}_{2}=\mathrm{mg}-\mathrm{ma}$ $\{\because$ Lift is moving down $\}$ $=9.8 \mathrm{~N}-4.9 \mathrm{~N}$ $=4.9 \mathrm{~N} $Ratio of the two tensions $\left(\frac{\mathrm{T}_{1}}{\mathrm{~T}_{2}}\right)=\frac{14.7 \mathrm{~N}}{4.9 \mathrm{~N}}$ $\frac{\mathrm{T}_{1}}{\mathrm{~T}_{2}}=3$ $\mathrm{T}_{1}: \mathrm{T}_{2}=3: 1$
WB JEE 2016
Mechanical Properties of Solids
140926
Which of the following substance has the highest elasticity?
1 Steel
2 Copper
3 Rubber
4 Sponge
Explanation:
A Modulus of elasticity (E) defined the value of elasticity, greater the value of $\mathrm{E}$ greater will be elasticity. Glass : 50 - $90 \mathrm{GPa}$ Rubber: $0.01-0.1 \mathrm{GPa}$ Steel : $210 \mathrm{GPa}$ Copper: $117 \mathrm{GPa}$ So, highest elasticity have steel.
WB JEE 2008
Mechanical Properties of Solids
140927
Which of the following statements is correct?
1 Hooke's law is applicable only within elastic limit
2 The adiabatic and isothermal elastic constants of a gas are equal
3 Young's modulus is dimensionless
4 Stress multiplied by strain is equal to the stored energy
Explanation:
A By Hooke's law, $\text { Elastic modulus }=\frac{\text { Stress }}{\text { Strain }}$ Hooke's law only works up to a certain limit after which the stress-strain graph does not follow the general pattern. The limit till which the Hooke's law is valid is known as elastic limit. So, statement (a) Hooke's law is applicable only within the elastic limit is correct. Let us consider option (b), The adiabatic constant of a gas is different from the isothermal elastic constant of a gas. So option (b) is incorrect. Let us consider option (c), Dimension of Young's modulus is $\mathrm{ML}^{-1} \mathrm{~T}^{-2}$. So option (c) is incorrect. Let us consider option (d) The half of stress multiplied by strain is elastic stored energy per unit volume. So, statement (d) is incorrect. Therefore, the correct option is (a).
