367511
A physical quantity \({X}\) is given by \({X=\dfrac{2 k^{3} l^{2}}{m \sqrt{n}}}\)The percentage error in the measurements of \({k, l, m}\) and \({n}\) are \({1 \%, 2 \%, 3 \%}\) and \({4 \%}\), respectively. The value of \({X}\) is uncertain by
367512
A thin copper wire of length \(L\) increases in length by 3% when heated from \({T_1}\) to \({T_2}\). If a copper cube having side 10 \(L\) is heated from \({T_1}\) to \({T_2}\), what will be the percentage change in area of one face of the cube?
1 \(6\,\% \)
2 \(3\,\% \)
3 \(2\,\% \)
4 \(4\,\% \)
Explanation:
Area \(A = 10L \times 10L = 100{L^2}\) Fractional change in the area is \(\frac{{\Delta A}}{A} = 2\frac{{\Delta L}}{L}\) Percentage change in area \( = \frac{{\Delta A}}{A} \times 100 = 2 \times \frac{{\Delta L}}{L} \times 100 = 2 \times 3\% = 6\% \)
PHXI02:UNITS AND MEASUREMENTS
367513
A body of mass \((5 \pm 0.5)kg\) is moving with a velocity of \((20 \pm 0.4)m{\rm{/}}s\). Its kinetic energy will be
1 \((1000 \pm 140) J\)
2 \((1000 \pm 0.14) J\)
3 \((500 \pm 0.14) J\)
4 \((500 \pm 140) J\)
Explanation:
Kinetic energy, \(K=\dfrac{1}{2} m v^{2}=\dfrac{1}{2} \times 5 \times 20 \times 20=1000 J\) We can find the error as follows \(\Rightarrow \dfrac{\Delta K}{K}=\dfrac{\Delta m}{m}+\dfrac{2 \Delta v}{v}\) \(=\dfrac{0.5}{5}+2 \times \dfrac{0.4}{20}=0.1+0.04\) \( \Rightarrow \Delta K = (0.14) \times 1000 = 140\;J\) \(\therefore K^{\prime}=K \pm \Delta K=(1000 \pm 140) J\) So, correct option is (1).
JEE - 2023
PHXI02:UNITS AND MEASUREMENTS
367514
Statement A : When a quantity appears with a power \(x\) greater than one in an expression, its error contribition to the final result increases \(x\) times. Statement B : In all mathematical operations, the errors are of additive in nature.
1 Statement A is correct but Statement B is incorrect.
2 Statement A is incorrect but Statement B is correct.
3 Both Statements are correct.
4 Both Statements are incorrect.
Explanation:
In all mathematical operations, the errors are of additive nature. When a quantity appears with a power \(x\) greater than one in an expression, its error contribution to the final result increases \(x\) times. So, quantities with higher power in the expression should be measured with maximum accuracy. Therefore, option (3) is correct.
PHXI02:UNITS AND MEASUREMENTS
367515
In a circuit, potential difference across resistance, is \(V = \left( {4 \pm 0.25} \right)V\) and current in resistance, \(I = \left( {1 \pm 0.1} \right)A.\) What is the value of resistance with its percentage error?
367511
A physical quantity \({X}\) is given by \({X=\dfrac{2 k^{3} l^{2}}{m \sqrt{n}}}\)The percentage error in the measurements of \({k, l, m}\) and \({n}\) are \({1 \%, 2 \%, 3 \%}\) and \({4 \%}\), respectively. The value of \({X}\) is uncertain by
367512
A thin copper wire of length \(L\) increases in length by 3% when heated from \({T_1}\) to \({T_2}\). If a copper cube having side 10 \(L\) is heated from \({T_1}\) to \({T_2}\), what will be the percentage change in area of one face of the cube?
1 \(6\,\% \)
2 \(3\,\% \)
3 \(2\,\% \)
4 \(4\,\% \)
Explanation:
Area \(A = 10L \times 10L = 100{L^2}\) Fractional change in the area is \(\frac{{\Delta A}}{A} = 2\frac{{\Delta L}}{L}\) Percentage change in area \( = \frac{{\Delta A}}{A} \times 100 = 2 \times \frac{{\Delta L}}{L} \times 100 = 2 \times 3\% = 6\% \)
PHXI02:UNITS AND MEASUREMENTS
367513
A body of mass \((5 \pm 0.5)kg\) is moving with a velocity of \((20 \pm 0.4)m{\rm{/}}s\). Its kinetic energy will be
1 \((1000 \pm 140) J\)
2 \((1000 \pm 0.14) J\)
3 \((500 \pm 0.14) J\)
4 \((500 \pm 140) J\)
Explanation:
Kinetic energy, \(K=\dfrac{1}{2} m v^{2}=\dfrac{1}{2} \times 5 \times 20 \times 20=1000 J\) We can find the error as follows \(\Rightarrow \dfrac{\Delta K}{K}=\dfrac{\Delta m}{m}+\dfrac{2 \Delta v}{v}\) \(=\dfrac{0.5}{5}+2 \times \dfrac{0.4}{20}=0.1+0.04\) \( \Rightarrow \Delta K = (0.14) \times 1000 = 140\;J\) \(\therefore K^{\prime}=K \pm \Delta K=(1000 \pm 140) J\) So, correct option is (1).
JEE - 2023
PHXI02:UNITS AND MEASUREMENTS
367514
Statement A : When a quantity appears with a power \(x\) greater than one in an expression, its error contribition to the final result increases \(x\) times. Statement B : In all mathematical operations, the errors are of additive in nature.
1 Statement A is correct but Statement B is incorrect.
2 Statement A is incorrect but Statement B is correct.
3 Both Statements are correct.
4 Both Statements are incorrect.
Explanation:
In all mathematical operations, the errors are of additive nature. When a quantity appears with a power \(x\) greater than one in an expression, its error contribution to the final result increases \(x\) times. So, quantities with higher power in the expression should be measured with maximum accuracy. Therefore, option (3) is correct.
PHXI02:UNITS AND MEASUREMENTS
367515
In a circuit, potential difference across resistance, is \(V = \left( {4 \pm 0.25} \right)V\) and current in resistance, \(I = \left( {1 \pm 0.1} \right)A.\) What is the value of resistance with its percentage error?
367511
A physical quantity \({X}\) is given by \({X=\dfrac{2 k^{3} l^{2}}{m \sqrt{n}}}\)The percentage error in the measurements of \({k, l, m}\) and \({n}\) are \({1 \%, 2 \%, 3 \%}\) and \({4 \%}\), respectively. The value of \({X}\) is uncertain by
367512
A thin copper wire of length \(L\) increases in length by 3% when heated from \({T_1}\) to \({T_2}\). If a copper cube having side 10 \(L\) is heated from \({T_1}\) to \({T_2}\), what will be the percentage change in area of one face of the cube?
1 \(6\,\% \)
2 \(3\,\% \)
3 \(2\,\% \)
4 \(4\,\% \)
Explanation:
Area \(A = 10L \times 10L = 100{L^2}\) Fractional change in the area is \(\frac{{\Delta A}}{A} = 2\frac{{\Delta L}}{L}\) Percentage change in area \( = \frac{{\Delta A}}{A} \times 100 = 2 \times \frac{{\Delta L}}{L} \times 100 = 2 \times 3\% = 6\% \)
PHXI02:UNITS AND MEASUREMENTS
367513
A body of mass \((5 \pm 0.5)kg\) is moving with a velocity of \((20 \pm 0.4)m{\rm{/}}s\). Its kinetic energy will be
1 \((1000 \pm 140) J\)
2 \((1000 \pm 0.14) J\)
3 \((500 \pm 0.14) J\)
4 \((500 \pm 140) J\)
Explanation:
Kinetic energy, \(K=\dfrac{1}{2} m v^{2}=\dfrac{1}{2} \times 5 \times 20 \times 20=1000 J\) We can find the error as follows \(\Rightarrow \dfrac{\Delta K}{K}=\dfrac{\Delta m}{m}+\dfrac{2 \Delta v}{v}\) \(=\dfrac{0.5}{5}+2 \times \dfrac{0.4}{20}=0.1+0.04\) \( \Rightarrow \Delta K = (0.14) \times 1000 = 140\;J\) \(\therefore K^{\prime}=K \pm \Delta K=(1000 \pm 140) J\) So, correct option is (1).
JEE - 2023
PHXI02:UNITS AND MEASUREMENTS
367514
Statement A : When a quantity appears with a power \(x\) greater than one in an expression, its error contribition to the final result increases \(x\) times. Statement B : In all mathematical operations, the errors are of additive in nature.
1 Statement A is correct but Statement B is incorrect.
2 Statement A is incorrect but Statement B is correct.
3 Both Statements are correct.
4 Both Statements are incorrect.
Explanation:
In all mathematical operations, the errors are of additive nature. When a quantity appears with a power \(x\) greater than one in an expression, its error contribution to the final result increases \(x\) times. So, quantities with higher power in the expression should be measured with maximum accuracy. Therefore, option (3) is correct.
PHXI02:UNITS AND MEASUREMENTS
367515
In a circuit, potential difference across resistance, is \(V = \left( {4 \pm 0.25} \right)V\) and current in resistance, \(I = \left( {1 \pm 0.1} \right)A.\) What is the value of resistance with its percentage error?
367511
A physical quantity \({X}\) is given by \({X=\dfrac{2 k^{3} l^{2}}{m \sqrt{n}}}\)The percentage error in the measurements of \({k, l, m}\) and \({n}\) are \({1 \%, 2 \%, 3 \%}\) and \({4 \%}\), respectively. The value of \({X}\) is uncertain by
367512
A thin copper wire of length \(L\) increases in length by 3% when heated from \({T_1}\) to \({T_2}\). If a copper cube having side 10 \(L\) is heated from \({T_1}\) to \({T_2}\), what will be the percentage change in area of one face of the cube?
1 \(6\,\% \)
2 \(3\,\% \)
3 \(2\,\% \)
4 \(4\,\% \)
Explanation:
Area \(A = 10L \times 10L = 100{L^2}\) Fractional change in the area is \(\frac{{\Delta A}}{A} = 2\frac{{\Delta L}}{L}\) Percentage change in area \( = \frac{{\Delta A}}{A} \times 100 = 2 \times \frac{{\Delta L}}{L} \times 100 = 2 \times 3\% = 6\% \)
PHXI02:UNITS AND MEASUREMENTS
367513
A body of mass \((5 \pm 0.5)kg\) is moving with a velocity of \((20 \pm 0.4)m{\rm{/}}s\). Its kinetic energy will be
1 \((1000 \pm 140) J\)
2 \((1000 \pm 0.14) J\)
3 \((500 \pm 0.14) J\)
4 \((500 \pm 140) J\)
Explanation:
Kinetic energy, \(K=\dfrac{1}{2} m v^{2}=\dfrac{1}{2} \times 5 \times 20 \times 20=1000 J\) We can find the error as follows \(\Rightarrow \dfrac{\Delta K}{K}=\dfrac{\Delta m}{m}+\dfrac{2 \Delta v}{v}\) \(=\dfrac{0.5}{5}+2 \times \dfrac{0.4}{20}=0.1+0.04\) \( \Rightarrow \Delta K = (0.14) \times 1000 = 140\;J\) \(\therefore K^{\prime}=K \pm \Delta K=(1000 \pm 140) J\) So, correct option is (1).
JEE - 2023
PHXI02:UNITS AND MEASUREMENTS
367514
Statement A : When a quantity appears with a power \(x\) greater than one in an expression, its error contribition to the final result increases \(x\) times. Statement B : In all mathematical operations, the errors are of additive in nature.
1 Statement A is correct but Statement B is incorrect.
2 Statement A is incorrect but Statement B is correct.
3 Both Statements are correct.
4 Both Statements are incorrect.
Explanation:
In all mathematical operations, the errors are of additive nature. When a quantity appears with a power \(x\) greater than one in an expression, its error contribution to the final result increases \(x\) times. So, quantities with higher power in the expression should be measured with maximum accuracy. Therefore, option (3) is correct.
PHXI02:UNITS AND MEASUREMENTS
367515
In a circuit, potential difference across resistance, is \(V = \left( {4 \pm 0.25} \right)V\) and current in resistance, \(I = \left( {1 \pm 0.1} \right)A.\) What is the value of resistance with its percentage error?
367511
A physical quantity \({X}\) is given by \({X=\dfrac{2 k^{3} l^{2}}{m \sqrt{n}}}\)The percentage error in the measurements of \({k, l, m}\) and \({n}\) are \({1 \%, 2 \%, 3 \%}\) and \({4 \%}\), respectively. The value of \({X}\) is uncertain by
367512
A thin copper wire of length \(L\) increases in length by 3% when heated from \({T_1}\) to \({T_2}\). If a copper cube having side 10 \(L\) is heated from \({T_1}\) to \({T_2}\), what will be the percentage change in area of one face of the cube?
1 \(6\,\% \)
2 \(3\,\% \)
3 \(2\,\% \)
4 \(4\,\% \)
Explanation:
Area \(A = 10L \times 10L = 100{L^2}\) Fractional change in the area is \(\frac{{\Delta A}}{A} = 2\frac{{\Delta L}}{L}\) Percentage change in area \( = \frac{{\Delta A}}{A} \times 100 = 2 \times \frac{{\Delta L}}{L} \times 100 = 2 \times 3\% = 6\% \)
PHXI02:UNITS AND MEASUREMENTS
367513
A body of mass \((5 \pm 0.5)kg\) is moving with a velocity of \((20 \pm 0.4)m{\rm{/}}s\). Its kinetic energy will be
1 \((1000 \pm 140) J\)
2 \((1000 \pm 0.14) J\)
3 \((500 \pm 0.14) J\)
4 \((500 \pm 140) J\)
Explanation:
Kinetic energy, \(K=\dfrac{1}{2} m v^{2}=\dfrac{1}{2} \times 5 \times 20 \times 20=1000 J\) We can find the error as follows \(\Rightarrow \dfrac{\Delta K}{K}=\dfrac{\Delta m}{m}+\dfrac{2 \Delta v}{v}\) \(=\dfrac{0.5}{5}+2 \times \dfrac{0.4}{20}=0.1+0.04\) \( \Rightarrow \Delta K = (0.14) \times 1000 = 140\;J\) \(\therefore K^{\prime}=K \pm \Delta K=(1000 \pm 140) J\) So, correct option is (1).
JEE - 2023
PHXI02:UNITS AND MEASUREMENTS
367514
Statement A : When a quantity appears with a power \(x\) greater than one in an expression, its error contribition to the final result increases \(x\) times. Statement B : In all mathematical operations, the errors are of additive in nature.
1 Statement A is correct but Statement B is incorrect.
2 Statement A is incorrect but Statement B is correct.
3 Both Statements are correct.
4 Both Statements are incorrect.
Explanation:
In all mathematical operations, the errors are of additive nature. When a quantity appears with a power \(x\) greater than one in an expression, its error contribution to the final result increases \(x\) times. So, quantities with higher power in the expression should be measured with maximum accuracy. Therefore, option (3) is correct.
PHXI02:UNITS AND MEASUREMENTS
367515
In a circuit, potential difference across resistance, is \(V = \left( {4 \pm 0.25} \right)V\) and current in resistance, \(I = \left( {1 \pm 0.1} \right)A.\) What is the value of resistance with its percentage error?
