NEET Test Series from KOTA - 10 Papers In MS WORD
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PHXI02:UNITS AND MEASUREMENTS
367328
If \(y = a{t^2} + b{t^3}\) where \(y\) is the distance travelled by the body in meters while \(t\) is in seconds then the unit of \(b\) is
1 \(m{s^2}\)
2 \(m{s^3}\)
3 \(m{s^{ - 3}}\)
4 \(m{s^{ - 2}}\)
Explanation:
\(b{t^3} = m \Rightarrow b = \frac{m}{{{t^3}}} = m{s^{ - 3}}\)
PHXI02:UNITS AND MEASUREMENTS
367329
Assertion : Force can be added to pressure. Reason : Force and pressure have different dimensions.
1 Both assertion and reason are correct and reason is the correct explanation of assertion.
2 Both assertion and reason are correct but reason is not the correct explanation of assertion.
3 Assertion is correct but reason is incorrect.
4 Assertion is incorrect but reason is correct.
Explanation:
The dimensions of force are \(\left[ {ML{T^{ - 2}}} \right]\). Dimensions of pressure are \(\left[ {M{L^{ - 1}}{T^{ - 2}}} \right]\) . Quantities with different dimensions cannot be added. So option (4) is correct.
PHXI02:UNITS AND MEASUREMENTS
367330
If the formula, \(X=3 Y Z^{2}, X\) and \(Z\) have dimensions of capacitance and magnetic induction. The dimensions of \(Y\) in \(M K S Q\) system are
1 \(\left[M^{-3} L^{-2} T^{4} Q^{4}\right]\)
2 \(\left[M L^{2} T^{8} Q^{4}\right]\)
3 \(\left[M^{-2} L^{-3} T^{2} Q^{4}\right]\)
4 \(\left[M^{-2} L^{-2} T Q^{2}\right]\)
Explanation:
According to question, \([X]=[C]=\left[M^{-1} L^{-2} T^{2} Q^{2}\right]\) and \([Z]=[B]=\left[M T^{-1} Q^{-1}\right]\) \(\because Y=\dfrac{[X]}{\left[Z^{2}\right]}\) \(Y=\dfrac{\left[M^{-1} L^{-2} T^{2} Q^{2}\right]}{\left[M^{2} T^{-2} Q^{-2}\right]}, Y=\left[M^{-3} L^{-2} T^{4} Q^{4}\right]\)
AIIMS - 2018
PHXI02:UNITS AND MEASUREMENTS
367331
Assertion : In the expression \(F=6 \pi r v \eta\), the dimension of \(\eta\) are \(\left[M L^{-1} T^{-1}\right]\). Reason : The coefficient of viscosity and linear momentum have same dimensions.
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:
\(F=6 \pi r v \eta \Rightarrow \eta=\dfrac{F}{6 \pi r v}\). Substituting the dimensions of all the terms involved on R.H.S. \(\eta=\dfrac{\left[M L T^{-2}\right]}{[L]\left[L T^{-1}\right]}=\left[M L^{-1} T^{-1}\right] \quad(\because 6 \pi\) is a unitless constant.) Dimensions of momentum \(=\) mass \(\times\) velocity \(=\left[M L T^{-1}\right]\) i.e. dimensions of \(\eta\) is not equal to dimensions of momentum. So correct option is (3)
367328
If \(y = a{t^2} + b{t^3}\) where \(y\) is the distance travelled by the body in meters while \(t\) is in seconds then the unit of \(b\) is
1 \(m{s^2}\)
2 \(m{s^3}\)
3 \(m{s^{ - 3}}\)
4 \(m{s^{ - 2}}\)
Explanation:
\(b{t^3} = m \Rightarrow b = \frac{m}{{{t^3}}} = m{s^{ - 3}}\)
PHXI02:UNITS AND MEASUREMENTS
367329
Assertion : Force can be added to pressure. Reason : Force and pressure have different dimensions.
1 Both assertion and reason are correct and reason is the correct explanation of assertion.
2 Both assertion and reason are correct but reason is not the correct explanation of assertion.
3 Assertion is correct but reason is incorrect.
4 Assertion is incorrect but reason is correct.
Explanation:
The dimensions of force are \(\left[ {ML{T^{ - 2}}} \right]\). Dimensions of pressure are \(\left[ {M{L^{ - 1}}{T^{ - 2}}} \right]\) . Quantities with different dimensions cannot be added. So option (4) is correct.
PHXI02:UNITS AND MEASUREMENTS
367330
If the formula, \(X=3 Y Z^{2}, X\) and \(Z\) have dimensions of capacitance and magnetic induction. The dimensions of \(Y\) in \(M K S Q\) system are
1 \(\left[M^{-3} L^{-2} T^{4} Q^{4}\right]\)
2 \(\left[M L^{2} T^{8} Q^{4}\right]\)
3 \(\left[M^{-2} L^{-3} T^{2} Q^{4}\right]\)
4 \(\left[M^{-2} L^{-2} T Q^{2}\right]\)
Explanation:
According to question, \([X]=[C]=\left[M^{-1} L^{-2} T^{2} Q^{2}\right]\) and \([Z]=[B]=\left[M T^{-1} Q^{-1}\right]\) \(\because Y=\dfrac{[X]}{\left[Z^{2}\right]}\) \(Y=\dfrac{\left[M^{-1} L^{-2} T^{2} Q^{2}\right]}{\left[M^{2} T^{-2} Q^{-2}\right]}, Y=\left[M^{-3} L^{-2} T^{4} Q^{4}\right]\)
AIIMS - 2018
PHXI02:UNITS AND MEASUREMENTS
367331
Assertion : In the expression \(F=6 \pi r v \eta\), the dimension of \(\eta\) are \(\left[M L^{-1} T^{-1}\right]\). Reason : The coefficient of viscosity and linear momentum have same dimensions.
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:
\(F=6 \pi r v \eta \Rightarrow \eta=\dfrac{F}{6 \pi r v}\). Substituting the dimensions of all the terms involved on R.H.S. \(\eta=\dfrac{\left[M L T^{-2}\right]}{[L]\left[L T^{-1}\right]}=\left[M L^{-1} T^{-1}\right] \quad(\because 6 \pi\) is a unitless constant.) Dimensions of momentum \(=\) mass \(\times\) velocity \(=\left[M L T^{-1}\right]\) i.e. dimensions of \(\eta\) is not equal to dimensions of momentum. So correct option is (3)
367328
If \(y = a{t^2} + b{t^3}\) where \(y\) is the distance travelled by the body in meters while \(t\) is in seconds then the unit of \(b\) is
1 \(m{s^2}\)
2 \(m{s^3}\)
3 \(m{s^{ - 3}}\)
4 \(m{s^{ - 2}}\)
Explanation:
\(b{t^3} = m \Rightarrow b = \frac{m}{{{t^3}}} = m{s^{ - 3}}\)
PHXI02:UNITS AND MEASUREMENTS
367329
Assertion : Force can be added to pressure. Reason : Force and pressure have different dimensions.
1 Both assertion and reason are correct and reason is the correct explanation of assertion.
2 Both assertion and reason are correct but reason is not the correct explanation of assertion.
3 Assertion is correct but reason is incorrect.
4 Assertion is incorrect but reason is correct.
Explanation:
The dimensions of force are \(\left[ {ML{T^{ - 2}}} \right]\). Dimensions of pressure are \(\left[ {M{L^{ - 1}}{T^{ - 2}}} \right]\) . Quantities with different dimensions cannot be added. So option (4) is correct.
PHXI02:UNITS AND MEASUREMENTS
367330
If the formula, \(X=3 Y Z^{2}, X\) and \(Z\) have dimensions of capacitance and magnetic induction. The dimensions of \(Y\) in \(M K S Q\) system are
1 \(\left[M^{-3} L^{-2} T^{4} Q^{4}\right]\)
2 \(\left[M L^{2} T^{8} Q^{4}\right]\)
3 \(\left[M^{-2} L^{-3} T^{2} Q^{4}\right]\)
4 \(\left[M^{-2} L^{-2} T Q^{2}\right]\)
Explanation:
According to question, \([X]=[C]=\left[M^{-1} L^{-2} T^{2} Q^{2}\right]\) and \([Z]=[B]=\left[M T^{-1} Q^{-1}\right]\) \(\because Y=\dfrac{[X]}{\left[Z^{2}\right]}\) \(Y=\dfrac{\left[M^{-1} L^{-2} T^{2} Q^{2}\right]}{\left[M^{2} T^{-2} Q^{-2}\right]}, Y=\left[M^{-3} L^{-2} T^{4} Q^{4}\right]\)
AIIMS - 2018
PHXI02:UNITS AND MEASUREMENTS
367331
Assertion : In the expression \(F=6 \pi r v \eta\), the dimension of \(\eta\) are \(\left[M L^{-1} T^{-1}\right]\). Reason : The coefficient of viscosity and linear momentum have same dimensions.
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:
\(F=6 \pi r v \eta \Rightarrow \eta=\dfrac{F}{6 \pi r v}\). Substituting the dimensions of all the terms involved on R.H.S. \(\eta=\dfrac{\left[M L T^{-2}\right]}{[L]\left[L T^{-1}\right]}=\left[M L^{-1} T^{-1}\right] \quad(\because 6 \pi\) is a unitless constant.) Dimensions of momentum \(=\) mass \(\times\) velocity \(=\left[M L T^{-1}\right]\) i.e. dimensions of \(\eta\) is not equal to dimensions of momentum. So correct option is (3)
367328
If \(y = a{t^2} + b{t^3}\) where \(y\) is the distance travelled by the body in meters while \(t\) is in seconds then the unit of \(b\) is
1 \(m{s^2}\)
2 \(m{s^3}\)
3 \(m{s^{ - 3}}\)
4 \(m{s^{ - 2}}\)
Explanation:
\(b{t^3} = m \Rightarrow b = \frac{m}{{{t^3}}} = m{s^{ - 3}}\)
PHXI02:UNITS AND MEASUREMENTS
367329
Assertion : Force can be added to pressure. Reason : Force and pressure have different dimensions.
1 Both assertion and reason are correct and reason is the correct explanation of assertion.
2 Both assertion and reason are correct but reason is not the correct explanation of assertion.
3 Assertion is correct but reason is incorrect.
4 Assertion is incorrect but reason is correct.
Explanation:
The dimensions of force are \(\left[ {ML{T^{ - 2}}} \right]\). Dimensions of pressure are \(\left[ {M{L^{ - 1}}{T^{ - 2}}} \right]\) . Quantities with different dimensions cannot be added. So option (4) is correct.
PHXI02:UNITS AND MEASUREMENTS
367330
If the formula, \(X=3 Y Z^{2}, X\) and \(Z\) have dimensions of capacitance and magnetic induction. The dimensions of \(Y\) in \(M K S Q\) system are
1 \(\left[M^{-3} L^{-2} T^{4} Q^{4}\right]\)
2 \(\left[M L^{2} T^{8} Q^{4}\right]\)
3 \(\left[M^{-2} L^{-3} T^{2} Q^{4}\right]\)
4 \(\left[M^{-2} L^{-2} T Q^{2}\right]\)
Explanation:
According to question, \([X]=[C]=\left[M^{-1} L^{-2} T^{2} Q^{2}\right]\) and \([Z]=[B]=\left[M T^{-1} Q^{-1}\right]\) \(\because Y=\dfrac{[X]}{\left[Z^{2}\right]}\) \(Y=\dfrac{\left[M^{-1} L^{-2} T^{2} Q^{2}\right]}{\left[M^{2} T^{-2} Q^{-2}\right]}, Y=\left[M^{-3} L^{-2} T^{4} Q^{4}\right]\)
AIIMS - 2018
PHXI02:UNITS AND MEASUREMENTS
367331
Assertion : In the expression \(F=6 \pi r v \eta\), the dimension of \(\eta\) are \(\left[M L^{-1} T^{-1}\right]\). Reason : The coefficient of viscosity and linear momentum have same dimensions.
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:
\(F=6 \pi r v \eta \Rightarrow \eta=\dfrac{F}{6 \pi r v}\). Substituting the dimensions of all the terms involved on R.H.S. \(\eta=\dfrac{\left[M L T^{-2}\right]}{[L]\left[L T^{-1}\right]}=\left[M L^{-1} T^{-1}\right] \quad(\because 6 \pi\) is a unitless constant.) Dimensions of momentum \(=\) mass \(\times\) velocity \(=\left[M L T^{-1}\right]\) i.e. dimensions of \(\eta\) is not equal to dimensions of momentum. So correct option is (3)
