360337
Statement A : Each vibrational mode has one degree of freedom. Statement B : By law of equipartition of energy, the energy for each degree of freedom in thermal equilibrium is \(3 k_{B} T\).
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:
By law of equipartition of energy, the energy for each degree of freedom in thermal equilibrium is \(\dfrac{1}{2} k_{B} T\). Each vibrational mode gives 2 degrees of freedom i.e., kinetic and potential energy modes, corresponding to the energy. Both statements are wrong. So option (4) is correct.
PHXI13:KINETIC THEORY
360338
Assertion : An undamped spring-mass system is simplest free vibration system. Reason : It has three degrees of freedom
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:
An undamped spring-mass system, characterized by a single degree of freedom. So correct option is (3).
PHXI13:KINETIC THEORY
360339
The translational degrees of freedom \({\left(f_{t}\right)}\) and rotational degrees of freedom \({\left(f_{r}\right)}\) of \({\rm{C}}{{\rm{H}}_4}\) molecule are
1 \({f_{t}=2}\) and \({f_{r}=2}\)
2 \({f_{t}=3}\) and \({f_{r}=2}\)
3 \({f_{t}=2}\) and \({f_{r}=3}\)
4 \({f_{t}=3}\) and \({f_{r}=3}\)
Explanation:
\({\rm{C}}{{\rm{H}}_4}\) is a polyatomic and non linear molecule. Translational degrees of freedom \({=3}\) Rotational degrees of freedom \({=3}\) \({\therefore \quad f_{t}=3}\) and \({f_{r}=3}\) So, Correct option is (4)
JEE - 2024
PHXI13:KINETIC THEORY
360340
A diatomic molecule has how many degrees of freedom
1 6
2 4
3 5
4 3
Explanation:
A diatomic molecule has three translational and two rotational degrees of freedom. Hence total degrees of freedom \(f=3+2=5\)
PHXI13:KINETIC THEORY
360341
Assertion : The number of degrees of freedom of a linear triatomic molecule is 7 . Reason : The number of degree of freedom depends on total number of particle in the system.
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:
The number \((f)\) of degrees of freedom depends on atomicity the molecular structure and can vary for different molecules. In the case of a linear triatomic molecule, there are two rotational, three translational, and two vibrational degrees of freedom that add up to a total of \(7,\left(P \propto \dfrac{1}{V}\right.\) at \(T=\) constant \() \quad\) value of \(f\) does not depend on total number of particles. So correct option is (3).
360337
Statement A : Each vibrational mode has one degree of freedom. Statement B : By law of equipartition of energy, the energy for each degree of freedom in thermal equilibrium is \(3 k_{B} T\).
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:
By law of equipartition of energy, the energy for each degree of freedom in thermal equilibrium is \(\dfrac{1}{2} k_{B} T\). Each vibrational mode gives 2 degrees of freedom i.e., kinetic and potential energy modes, corresponding to the energy. Both statements are wrong. So option (4) is correct.
PHXI13:KINETIC THEORY
360338
Assertion : An undamped spring-mass system is simplest free vibration system. Reason : It has three degrees of freedom
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:
An undamped spring-mass system, characterized by a single degree of freedom. So correct option is (3).
PHXI13:KINETIC THEORY
360339
The translational degrees of freedom \({\left(f_{t}\right)}\) and rotational degrees of freedom \({\left(f_{r}\right)}\) of \({\rm{C}}{{\rm{H}}_4}\) molecule are
1 \({f_{t}=2}\) and \({f_{r}=2}\)
2 \({f_{t}=3}\) and \({f_{r}=2}\)
3 \({f_{t}=2}\) and \({f_{r}=3}\)
4 \({f_{t}=3}\) and \({f_{r}=3}\)
Explanation:
\({\rm{C}}{{\rm{H}}_4}\) is a polyatomic and non linear molecule. Translational degrees of freedom \({=3}\) Rotational degrees of freedom \({=3}\) \({\therefore \quad f_{t}=3}\) and \({f_{r}=3}\) So, Correct option is (4)
JEE - 2024
PHXI13:KINETIC THEORY
360340
A diatomic molecule has how many degrees of freedom
1 6
2 4
3 5
4 3
Explanation:
A diatomic molecule has three translational and two rotational degrees of freedom. Hence total degrees of freedom \(f=3+2=5\)
PHXI13:KINETIC THEORY
360341
Assertion : The number of degrees of freedom of a linear triatomic molecule is 7 . Reason : The number of degree of freedom depends on total number of particle in the system.
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:
The number \((f)\) of degrees of freedom depends on atomicity the molecular structure and can vary for different molecules. In the case of a linear triatomic molecule, there are two rotational, three translational, and two vibrational degrees of freedom that add up to a total of \(7,\left(P \propto \dfrac{1}{V}\right.\) at \(T=\) constant \() \quad\) value of \(f\) does not depend on total number of particles. So correct option is (3).
360337
Statement A : Each vibrational mode has one degree of freedom. Statement B : By law of equipartition of energy, the energy for each degree of freedom in thermal equilibrium is \(3 k_{B} T\).
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:
By law of equipartition of energy, the energy for each degree of freedom in thermal equilibrium is \(\dfrac{1}{2} k_{B} T\). Each vibrational mode gives 2 degrees of freedom i.e., kinetic and potential energy modes, corresponding to the energy. Both statements are wrong. So option (4) is correct.
PHXI13:KINETIC THEORY
360338
Assertion : An undamped spring-mass system is simplest free vibration system. Reason : It has three degrees of freedom
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:
An undamped spring-mass system, characterized by a single degree of freedom. So correct option is (3).
PHXI13:KINETIC THEORY
360339
The translational degrees of freedom \({\left(f_{t}\right)}\) and rotational degrees of freedom \({\left(f_{r}\right)}\) of \({\rm{C}}{{\rm{H}}_4}\) molecule are
1 \({f_{t}=2}\) and \({f_{r}=2}\)
2 \({f_{t}=3}\) and \({f_{r}=2}\)
3 \({f_{t}=2}\) and \({f_{r}=3}\)
4 \({f_{t}=3}\) and \({f_{r}=3}\)
Explanation:
\({\rm{C}}{{\rm{H}}_4}\) is a polyatomic and non linear molecule. Translational degrees of freedom \({=3}\) Rotational degrees of freedom \({=3}\) \({\therefore \quad f_{t}=3}\) and \({f_{r}=3}\) So, Correct option is (4)
JEE - 2024
PHXI13:KINETIC THEORY
360340
A diatomic molecule has how many degrees of freedom
1 6
2 4
3 5
4 3
Explanation:
A diatomic molecule has three translational and two rotational degrees of freedom. Hence total degrees of freedom \(f=3+2=5\)
PHXI13:KINETIC THEORY
360341
Assertion : The number of degrees of freedom of a linear triatomic molecule is 7 . Reason : The number of degree of freedom depends on total number of particle in the system.
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:
The number \((f)\) of degrees of freedom depends on atomicity the molecular structure and can vary for different molecules. In the case of a linear triatomic molecule, there are two rotational, three translational, and two vibrational degrees of freedom that add up to a total of \(7,\left(P \propto \dfrac{1}{V}\right.\) at \(T=\) constant \() \quad\) value of \(f\) does not depend on total number of particles. So correct option is (3).
NEET Test Series from KOTA - 10 Papers In MS WORD
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PHXI13:KINETIC THEORY
360337
Statement A : Each vibrational mode has one degree of freedom. Statement B : By law of equipartition of energy, the energy for each degree of freedom in thermal equilibrium is \(3 k_{B} T\).
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:
By law of equipartition of energy, the energy for each degree of freedom in thermal equilibrium is \(\dfrac{1}{2} k_{B} T\). Each vibrational mode gives 2 degrees of freedom i.e., kinetic and potential energy modes, corresponding to the energy. Both statements are wrong. So option (4) is correct.
PHXI13:KINETIC THEORY
360338
Assertion : An undamped spring-mass system is simplest free vibration system. Reason : It has three degrees of freedom
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:
An undamped spring-mass system, characterized by a single degree of freedom. So correct option is (3).
PHXI13:KINETIC THEORY
360339
The translational degrees of freedom \({\left(f_{t}\right)}\) and rotational degrees of freedom \({\left(f_{r}\right)}\) of \({\rm{C}}{{\rm{H}}_4}\) molecule are
1 \({f_{t}=2}\) and \({f_{r}=2}\)
2 \({f_{t}=3}\) and \({f_{r}=2}\)
3 \({f_{t}=2}\) and \({f_{r}=3}\)
4 \({f_{t}=3}\) and \({f_{r}=3}\)
Explanation:
\({\rm{C}}{{\rm{H}}_4}\) is a polyatomic and non linear molecule. Translational degrees of freedom \({=3}\) Rotational degrees of freedom \({=3}\) \({\therefore \quad f_{t}=3}\) and \({f_{r}=3}\) So, Correct option is (4)
JEE - 2024
PHXI13:KINETIC THEORY
360340
A diatomic molecule has how many degrees of freedom
1 6
2 4
3 5
4 3
Explanation:
A diatomic molecule has three translational and two rotational degrees of freedom. Hence total degrees of freedom \(f=3+2=5\)
PHXI13:KINETIC THEORY
360341
Assertion : The number of degrees of freedom of a linear triatomic molecule is 7 . Reason : The number of degree of freedom depends on total number of particle in the system.
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:
The number \((f)\) of degrees of freedom depends on atomicity the molecular structure and can vary for different molecules. In the case of a linear triatomic molecule, there are two rotational, three translational, and two vibrational degrees of freedom that add up to a total of \(7,\left(P \propto \dfrac{1}{V}\right.\) at \(T=\) constant \() \quad\) value of \(f\) does not depend on total number of particles. So correct option is (3).
360337
Statement A : Each vibrational mode has one degree of freedom. Statement B : By law of equipartition of energy, the energy for each degree of freedom in thermal equilibrium is \(3 k_{B} T\).
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:
By law of equipartition of energy, the energy for each degree of freedom in thermal equilibrium is \(\dfrac{1}{2} k_{B} T\). Each vibrational mode gives 2 degrees of freedom i.e., kinetic and potential energy modes, corresponding to the energy. Both statements are wrong. So option (4) is correct.
PHXI13:KINETIC THEORY
360338
Assertion : An undamped spring-mass system is simplest free vibration system. Reason : It has three degrees of freedom
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:
An undamped spring-mass system, characterized by a single degree of freedom. So correct option is (3).
PHXI13:KINETIC THEORY
360339
The translational degrees of freedom \({\left(f_{t}\right)}\) and rotational degrees of freedom \({\left(f_{r}\right)}\) of \({\rm{C}}{{\rm{H}}_4}\) molecule are
1 \({f_{t}=2}\) and \({f_{r}=2}\)
2 \({f_{t}=3}\) and \({f_{r}=2}\)
3 \({f_{t}=2}\) and \({f_{r}=3}\)
4 \({f_{t}=3}\) and \({f_{r}=3}\)
Explanation:
\({\rm{C}}{{\rm{H}}_4}\) is a polyatomic and non linear molecule. Translational degrees of freedom \({=3}\) Rotational degrees of freedom \({=3}\) \({\therefore \quad f_{t}=3}\) and \({f_{r}=3}\) So, Correct option is (4)
JEE - 2024
PHXI13:KINETIC THEORY
360340
A diatomic molecule has how many degrees of freedom
1 6
2 4
3 5
4 3
Explanation:
A diatomic molecule has three translational and two rotational degrees of freedom. Hence total degrees of freedom \(f=3+2=5\)
PHXI13:KINETIC THEORY
360341
Assertion : The number of degrees of freedom of a linear triatomic molecule is 7 . Reason : The number of degree of freedom depends on total number of particle in the system.
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:
The number \((f)\) of degrees of freedom depends on atomicity the molecular structure and can vary for different molecules. In the case of a linear triatomic molecule, there are two rotational, three translational, and two vibrational degrees of freedom that add up to a total of \(7,\left(P \propto \dfrac{1}{V}\right.\) at \(T=\) constant \() \quad\) value of \(f\) does not depend on total number of particles. So correct option is (3).