369775
Assertion : When a spring is loaded, then shearing stress is produced in it. Reason : Shape of spring remains unchanged under the application of tangential stress.
1 Both Assertion and Reason are correct and Reason is the correct explanation of the Assertion.
2 Both Assertion and Reason are correct but Reason is not the correct explanation of the Assertion.
3 Assertion is correct but Reason is incorrect.
4 Assertion is incorrect but reason is correct.
Explanation:
When a spring is loaded, then shearing stress is produced, which changes the shape of spring. Therefore, Assertion is correct but Reason is incorrect. Option (3) is correct.
PHXI09:MECHANICAL PROPERTIES OF SOLIDS
369776
A river \(10\;m\) deep is flowing at \(5\;\,m/s\). The shearing strees between horizontal layers of the river ( \(\eta=10^{-3}\) SI units)
369777
Calculate the force \(F\) needed to punch a 1.46 \(cm\) diameter hole in a steel plate \(1.27\;cm\) thick. The ultimate shear strength of steel is \(345MN/{m^2}\).
1 \(300\,KN\)
2 \(200\,KN\)
3 \(350\,KN\)
4 \(225\,KN\)
Explanation:
\(\mathrm{F}>\) (shear stress) \(\times\) area \(\begin{gathered}\therefore \quad F_{\min }=\left(3.45 \times 10^{8}\right)(2 \pi r l) \\=\left(3.45 \times 10^{8}\right)\left(2 \times 3.14 \times 0.73 \times 10^{-2} \times 1.27 \times 10^{-2}\right) \\=200 K N\end{gathered}\)
PHXI09:MECHANICAL PROPERTIES OF SOLIDS
369778
The \(Y_{e q}\) of the composite rod is (assume A \(=\) Area of cross section of each rod), then\(x = {l_1} = {l_2} = 1\;m,F = 2\;N/{m^2},A = 1sq \cdot {m^2}\) \({Y_1} = 2 \times {10^{11}}\;N/{m^2},{Y_2} = 3 \times {10^{11}}\;N/{m^2}\)
1 \(2.4 \times {10^{11}}\;N/{m^2}\)
2 \(2.86 \times {10^{11}}\;N/{m^2}\)
3 \(2.88 \times {10^{11}}\;N/{m^2}\)
4 \(2.4 \times {10^8}\;N/{m^2}\)
Explanation:
The system can be considered as two springs connected in series. \(K = \frac{{{K_1}{K_2}}}{{{K_1} + {K_2}}}\) \({K_1} = \frac{{{Y_1}A}}{{{l_1}}},{K_2} = \frac{{{Y_2}A}}{{{l_2}}}\) \(K = \frac{{{Y_1}{Y_2}A}}{{{Y_1}{l_2} + {Y_2}{l_1}}} = \frac{{YA}}{{\left( {{l_1} + {l_2}} \right)}}\) \( \Rightarrow \quad Y = 2 \cdot 4 \times {10^{11}}\;N/{m^2}\)
PHXI09:MECHANICAL PROPERTIES OF SOLIDS
369779
A steel rod of length \(3\;m\) and cross-sectional area \(1{m^2}\) ia acted upon by forces shown in figure.Determine the elongation of the length BC of the bar. Take \(Y = 2.0 \times {10^{11}}\;N/{m^2}.\)
1 \(4.5 \times {10^{ - 7}}\;m\)
2 \(13 \times {10^{ - 7}}\;m\)
3 \(5 \times {10^{ - 7}}\;m\)
4 \(3.5 \times {10^{ - 7}}\;m\)
Explanation:
The bar is at equilibrium. The net force from right or left of a section of BC is \(70\,KN\). We know that the extension due to external forces F is given \(\Delta l = \frac{{Fl}}{{AY}};\quad \Delta {l_{BC}} = \frac{{\left( {70 \times {{10}^3}} \right) \times 1}}{{1 \times 2 \times {{10}^{11}}}} = 3.5 \times {10^{ - 7}}m\)
369775
Assertion : When a spring is loaded, then shearing stress is produced in it. Reason : Shape of spring remains unchanged under the application of tangential stress.
1 Both Assertion and Reason are correct and Reason is the correct explanation of the Assertion.
2 Both Assertion and Reason are correct but Reason is not the correct explanation of the Assertion.
3 Assertion is correct but Reason is incorrect.
4 Assertion is incorrect but reason is correct.
Explanation:
When a spring is loaded, then shearing stress is produced, which changes the shape of spring. Therefore, Assertion is correct but Reason is incorrect. Option (3) is correct.
PHXI09:MECHANICAL PROPERTIES OF SOLIDS
369776
A river \(10\;m\) deep is flowing at \(5\;\,m/s\). The shearing strees between horizontal layers of the river ( \(\eta=10^{-3}\) SI units)
369777
Calculate the force \(F\) needed to punch a 1.46 \(cm\) diameter hole in a steel plate \(1.27\;cm\) thick. The ultimate shear strength of steel is \(345MN/{m^2}\).
1 \(300\,KN\)
2 \(200\,KN\)
3 \(350\,KN\)
4 \(225\,KN\)
Explanation:
\(\mathrm{F}>\) (shear stress) \(\times\) area \(\begin{gathered}\therefore \quad F_{\min }=\left(3.45 \times 10^{8}\right)(2 \pi r l) \\=\left(3.45 \times 10^{8}\right)\left(2 \times 3.14 \times 0.73 \times 10^{-2} \times 1.27 \times 10^{-2}\right) \\=200 K N\end{gathered}\)
PHXI09:MECHANICAL PROPERTIES OF SOLIDS
369778
The \(Y_{e q}\) of the composite rod is (assume A \(=\) Area of cross section of each rod), then\(x = {l_1} = {l_2} = 1\;m,F = 2\;N/{m^2},A = 1sq \cdot {m^2}\) \({Y_1} = 2 \times {10^{11}}\;N/{m^2},{Y_2} = 3 \times {10^{11}}\;N/{m^2}\)
1 \(2.4 \times {10^{11}}\;N/{m^2}\)
2 \(2.86 \times {10^{11}}\;N/{m^2}\)
3 \(2.88 \times {10^{11}}\;N/{m^2}\)
4 \(2.4 \times {10^8}\;N/{m^2}\)
Explanation:
The system can be considered as two springs connected in series. \(K = \frac{{{K_1}{K_2}}}{{{K_1} + {K_2}}}\) \({K_1} = \frac{{{Y_1}A}}{{{l_1}}},{K_2} = \frac{{{Y_2}A}}{{{l_2}}}\) \(K = \frac{{{Y_1}{Y_2}A}}{{{Y_1}{l_2} + {Y_2}{l_1}}} = \frac{{YA}}{{\left( {{l_1} + {l_2}} \right)}}\) \( \Rightarrow \quad Y = 2 \cdot 4 \times {10^{11}}\;N/{m^2}\)
PHXI09:MECHANICAL PROPERTIES OF SOLIDS
369779
A steel rod of length \(3\;m\) and cross-sectional area \(1{m^2}\) ia acted upon by forces shown in figure.Determine the elongation of the length BC of the bar. Take \(Y = 2.0 \times {10^{11}}\;N/{m^2}.\)
1 \(4.5 \times {10^{ - 7}}\;m\)
2 \(13 \times {10^{ - 7}}\;m\)
3 \(5 \times {10^{ - 7}}\;m\)
4 \(3.5 \times {10^{ - 7}}\;m\)
Explanation:
The bar is at equilibrium. The net force from right or left of a section of BC is \(70\,KN\). We know that the extension due to external forces F is given \(\Delta l = \frac{{Fl}}{{AY}};\quad \Delta {l_{BC}} = \frac{{\left( {70 \times {{10}^3}} \right) \times 1}}{{1 \times 2 \times {{10}^{11}}}} = 3.5 \times {10^{ - 7}}m\)
369775
Assertion : When a spring is loaded, then shearing stress is produced in it. Reason : Shape of spring remains unchanged under the application of tangential stress.
1 Both Assertion and Reason are correct and Reason is the correct explanation of the Assertion.
2 Both Assertion and Reason are correct but Reason is not the correct explanation of the Assertion.
3 Assertion is correct but Reason is incorrect.
4 Assertion is incorrect but reason is correct.
Explanation:
When a spring is loaded, then shearing stress is produced, which changes the shape of spring. Therefore, Assertion is correct but Reason is incorrect. Option (3) is correct.
PHXI09:MECHANICAL PROPERTIES OF SOLIDS
369776
A river \(10\;m\) deep is flowing at \(5\;\,m/s\). The shearing strees between horizontal layers of the river ( \(\eta=10^{-3}\) SI units)
369777
Calculate the force \(F\) needed to punch a 1.46 \(cm\) diameter hole in a steel plate \(1.27\;cm\) thick. The ultimate shear strength of steel is \(345MN/{m^2}\).
1 \(300\,KN\)
2 \(200\,KN\)
3 \(350\,KN\)
4 \(225\,KN\)
Explanation:
\(\mathrm{F}>\) (shear stress) \(\times\) area \(\begin{gathered}\therefore \quad F_{\min }=\left(3.45 \times 10^{8}\right)(2 \pi r l) \\=\left(3.45 \times 10^{8}\right)\left(2 \times 3.14 \times 0.73 \times 10^{-2} \times 1.27 \times 10^{-2}\right) \\=200 K N\end{gathered}\)
PHXI09:MECHANICAL PROPERTIES OF SOLIDS
369778
The \(Y_{e q}\) of the composite rod is (assume A \(=\) Area of cross section of each rod), then\(x = {l_1} = {l_2} = 1\;m,F = 2\;N/{m^2},A = 1sq \cdot {m^2}\) \({Y_1} = 2 \times {10^{11}}\;N/{m^2},{Y_2} = 3 \times {10^{11}}\;N/{m^2}\)
1 \(2.4 \times {10^{11}}\;N/{m^2}\)
2 \(2.86 \times {10^{11}}\;N/{m^2}\)
3 \(2.88 \times {10^{11}}\;N/{m^2}\)
4 \(2.4 \times {10^8}\;N/{m^2}\)
Explanation:
The system can be considered as two springs connected in series. \(K = \frac{{{K_1}{K_2}}}{{{K_1} + {K_2}}}\) \({K_1} = \frac{{{Y_1}A}}{{{l_1}}},{K_2} = \frac{{{Y_2}A}}{{{l_2}}}\) \(K = \frac{{{Y_1}{Y_2}A}}{{{Y_1}{l_2} + {Y_2}{l_1}}} = \frac{{YA}}{{\left( {{l_1} + {l_2}} \right)}}\) \( \Rightarrow \quad Y = 2 \cdot 4 \times {10^{11}}\;N/{m^2}\)
PHXI09:MECHANICAL PROPERTIES OF SOLIDS
369779
A steel rod of length \(3\;m\) and cross-sectional area \(1{m^2}\) ia acted upon by forces shown in figure.Determine the elongation of the length BC of the bar. Take \(Y = 2.0 \times {10^{11}}\;N/{m^2}.\)
1 \(4.5 \times {10^{ - 7}}\;m\)
2 \(13 \times {10^{ - 7}}\;m\)
3 \(5 \times {10^{ - 7}}\;m\)
4 \(3.5 \times {10^{ - 7}}\;m\)
Explanation:
The bar is at equilibrium. The net force from right or left of a section of BC is \(70\,KN\). We know that the extension due to external forces F is given \(\Delta l = \frac{{Fl}}{{AY}};\quad \Delta {l_{BC}} = \frac{{\left( {70 \times {{10}^3}} \right) \times 1}}{{1 \times 2 \times {{10}^{11}}}} = 3.5 \times {10^{ - 7}}m\)
369775
Assertion : When a spring is loaded, then shearing stress is produced in it. Reason : Shape of spring remains unchanged under the application of tangential stress.
1 Both Assertion and Reason are correct and Reason is the correct explanation of the Assertion.
2 Both Assertion and Reason are correct but Reason is not the correct explanation of the Assertion.
3 Assertion is correct but Reason is incorrect.
4 Assertion is incorrect but reason is correct.
Explanation:
When a spring is loaded, then shearing stress is produced, which changes the shape of spring. Therefore, Assertion is correct but Reason is incorrect. Option (3) is correct.
PHXI09:MECHANICAL PROPERTIES OF SOLIDS
369776
A river \(10\;m\) deep is flowing at \(5\;\,m/s\). The shearing strees between horizontal layers of the river ( \(\eta=10^{-3}\) SI units)
369777
Calculate the force \(F\) needed to punch a 1.46 \(cm\) diameter hole in a steel plate \(1.27\;cm\) thick. The ultimate shear strength of steel is \(345MN/{m^2}\).
1 \(300\,KN\)
2 \(200\,KN\)
3 \(350\,KN\)
4 \(225\,KN\)
Explanation:
\(\mathrm{F}>\) (shear stress) \(\times\) area \(\begin{gathered}\therefore \quad F_{\min }=\left(3.45 \times 10^{8}\right)(2 \pi r l) \\=\left(3.45 \times 10^{8}\right)\left(2 \times 3.14 \times 0.73 \times 10^{-2} \times 1.27 \times 10^{-2}\right) \\=200 K N\end{gathered}\)
PHXI09:MECHANICAL PROPERTIES OF SOLIDS
369778
The \(Y_{e q}\) of the composite rod is (assume A \(=\) Area of cross section of each rod), then\(x = {l_1} = {l_2} = 1\;m,F = 2\;N/{m^2},A = 1sq \cdot {m^2}\) \({Y_1} = 2 \times {10^{11}}\;N/{m^2},{Y_2} = 3 \times {10^{11}}\;N/{m^2}\)
1 \(2.4 \times {10^{11}}\;N/{m^2}\)
2 \(2.86 \times {10^{11}}\;N/{m^2}\)
3 \(2.88 \times {10^{11}}\;N/{m^2}\)
4 \(2.4 \times {10^8}\;N/{m^2}\)
Explanation:
The system can be considered as two springs connected in series. \(K = \frac{{{K_1}{K_2}}}{{{K_1} + {K_2}}}\) \({K_1} = \frac{{{Y_1}A}}{{{l_1}}},{K_2} = \frac{{{Y_2}A}}{{{l_2}}}\) \(K = \frac{{{Y_1}{Y_2}A}}{{{Y_1}{l_2} + {Y_2}{l_1}}} = \frac{{YA}}{{\left( {{l_1} + {l_2}} \right)}}\) \( \Rightarrow \quad Y = 2 \cdot 4 \times {10^{11}}\;N/{m^2}\)
PHXI09:MECHANICAL PROPERTIES OF SOLIDS
369779
A steel rod of length \(3\;m\) and cross-sectional area \(1{m^2}\) ia acted upon by forces shown in figure.Determine the elongation of the length BC of the bar. Take \(Y = 2.0 \times {10^{11}}\;N/{m^2}.\)
1 \(4.5 \times {10^{ - 7}}\;m\)
2 \(13 \times {10^{ - 7}}\;m\)
3 \(5 \times {10^{ - 7}}\;m\)
4 \(3.5 \times {10^{ - 7}}\;m\)
Explanation:
The bar is at equilibrium. The net force from right or left of a section of BC is \(70\,KN\). We know that the extension due to external forces F is given \(\Delta l = \frac{{Fl}}{{AY}};\quad \Delta {l_{BC}} = \frac{{\left( {70 \times {{10}^3}} \right) \times 1}}{{1 \times 2 \times {{10}^{11}}}} = 3.5 \times {10^{ - 7}}m\)
369775
Assertion : When a spring is loaded, then shearing stress is produced in it. Reason : Shape of spring remains unchanged under the application of tangential stress.
1 Both Assertion and Reason are correct and Reason is the correct explanation of the Assertion.
2 Both Assertion and Reason are correct but Reason is not the correct explanation of the Assertion.
3 Assertion is correct but Reason is incorrect.
4 Assertion is incorrect but reason is correct.
Explanation:
When a spring is loaded, then shearing stress is produced, which changes the shape of spring. Therefore, Assertion is correct but Reason is incorrect. Option (3) is correct.
PHXI09:MECHANICAL PROPERTIES OF SOLIDS
369776
A river \(10\;m\) deep is flowing at \(5\;\,m/s\). The shearing strees between horizontal layers of the river ( \(\eta=10^{-3}\) SI units)
369777
Calculate the force \(F\) needed to punch a 1.46 \(cm\) diameter hole in a steel plate \(1.27\;cm\) thick. The ultimate shear strength of steel is \(345MN/{m^2}\).
1 \(300\,KN\)
2 \(200\,KN\)
3 \(350\,KN\)
4 \(225\,KN\)
Explanation:
\(\mathrm{F}>\) (shear stress) \(\times\) area \(\begin{gathered}\therefore \quad F_{\min }=\left(3.45 \times 10^{8}\right)(2 \pi r l) \\=\left(3.45 \times 10^{8}\right)\left(2 \times 3.14 \times 0.73 \times 10^{-2} \times 1.27 \times 10^{-2}\right) \\=200 K N\end{gathered}\)
PHXI09:MECHANICAL PROPERTIES OF SOLIDS
369778
The \(Y_{e q}\) of the composite rod is (assume A \(=\) Area of cross section of each rod), then\(x = {l_1} = {l_2} = 1\;m,F = 2\;N/{m^2},A = 1sq \cdot {m^2}\) \({Y_1} = 2 \times {10^{11}}\;N/{m^2},{Y_2} = 3 \times {10^{11}}\;N/{m^2}\)
1 \(2.4 \times {10^{11}}\;N/{m^2}\)
2 \(2.86 \times {10^{11}}\;N/{m^2}\)
3 \(2.88 \times {10^{11}}\;N/{m^2}\)
4 \(2.4 \times {10^8}\;N/{m^2}\)
Explanation:
The system can be considered as two springs connected in series. \(K = \frac{{{K_1}{K_2}}}{{{K_1} + {K_2}}}\) \({K_1} = \frac{{{Y_1}A}}{{{l_1}}},{K_2} = \frac{{{Y_2}A}}{{{l_2}}}\) \(K = \frac{{{Y_1}{Y_2}A}}{{{Y_1}{l_2} + {Y_2}{l_1}}} = \frac{{YA}}{{\left( {{l_1} + {l_2}} \right)}}\) \( \Rightarrow \quad Y = 2 \cdot 4 \times {10^{11}}\;N/{m^2}\)
PHXI09:MECHANICAL PROPERTIES OF SOLIDS
369779
A steel rod of length \(3\;m\) and cross-sectional area \(1{m^2}\) ia acted upon by forces shown in figure.Determine the elongation of the length BC of the bar. Take \(Y = 2.0 \times {10^{11}}\;N/{m^2}.\)
1 \(4.5 \times {10^{ - 7}}\;m\)
2 \(13 \times {10^{ - 7}}\;m\)
3 \(5 \times {10^{ - 7}}\;m\)
4 \(3.5 \times {10^{ - 7}}\;m\)
Explanation:
The bar is at equilibrium. The net force from right or left of a section of BC is \(70\,KN\). We know that the extension due to external forces F is given \(\Delta l = \frac{{Fl}}{{AY}};\quad \Delta {l_{BC}} = \frac{{\left( {70 \times {{10}^3}} \right) \times 1}}{{1 \times 2 \times {{10}^{11}}}} = 3.5 \times {10^{ - 7}}m\)
