355395
Work done by the conservative forces on a system is equal to
1 The change in kinetic energy of the system
2 The (\(-ve\)) of change in potential energy of the system
3 The (\(-ve\)) change in total mechanical energy of the system
4 None of the above
Explanation:
\(W=-\Delta U\)
PHXI06:WORK ENERGY AND POWER
355396
Assertion : Frictional forces are conservative forces. Reason : Potential energy can not be associated with frictional forces.
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:
For conservative force \(F\) there exists a function of potential energy \((U)\) such that magnitude of force is \(|F|=\dfrac{d U}{d r}\). Gravity and an electrostatic field in a vacuum are examples of conservative forces. However, any form of friction disrupts the field's conservativeness. Then, potential energy cannot be associated with frictional forces. So correct option is (4).
PHXI06:WORK ENERGY AND POWER
355397
Which of the following is a conservative force?
1 \(x y \hat{i}+4 \hat{j}\)
2 \(x y \hat{j}+x^{2} y^{2} \hat{j}\)
3 \(x^{2} y^{2} \hat{i}+x y \hat{j}\)
4 \(x^{2} y^{3} \hat{i}+y^{2} x^{3} \hat{j}\)
Explanation:
If the force \(\vec{F}=F_{x} \hat{i}+F_{y} \hat{j}\) is conservative then \(\dfrac{J F_{x}}{J y}=\dfrac{J F_{y}}{J x}\) For the force given in option (4) \(\begin{aligned}F_{x} & =x^{2} y^{3} \\\dfrac{J F_{x}}{J y} & =3 x^{2} y^{2} \\F_{y} & =y^{2} x^{3} \\\dfrac{J F_{y}}{J x} & =3 y^{2} x^{2} \\\Rightarrow \dfrac{J F_{x}}{J y} & =\dfrac{J F_{y}}{J x}\end{aligned}\) For the remaining forces the above condition is not fulfilled.
PHXI06:WORK ENERGY AND POWER
355398
Assertion : The work done by a conservative force such as gravity depends on the initial and final positions only. Reason : The work done by a force cannot be calculated if the nature of the force is not known.
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 work done by a force can be calculated sometimes even if the nature of the force is not known. Work done by conservative force depends on intial and final positions. So option (3) is correct.
355395
Work done by the conservative forces on a system is equal to
1 The change in kinetic energy of the system
2 The (\(-ve\)) of change in potential energy of the system
3 The (\(-ve\)) change in total mechanical energy of the system
4 None of the above
Explanation:
\(W=-\Delta U\)
PHXI06:WORK ENERGY AND POWER
355396
Assertion : Frictional forces are conservative forces. Reason : Potential energy can not be associated with frictional forces.
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:
For conservative force \(F\) there exists a function of potential energy \((U)\) such that magnitude of force is \(|F|=\dfrac{d U}{d r}\). Gravity and an electrostatic field in a vacuum are examples of conservative forces. However, any form of friction disrupts the field's conservativeness. Then, potential energy cannot be associated with frictional forces. So correct option is (4).
PHXI06:WORK ENERGY AND POWER
355397
Which of the following is a conservative force?
1 \(x y \hat{i}+4 \hat{j}\)
2 \(x y \hat{j}+x^{2} y^{2} \hat{j}\)
3 \(x^{2} y^{2} \hat{i}+x y \hat{j}\)
4 \(x^{2} y^{3} \hat{i}+y^{2} x^{3} \hat{j}\)
Explanation:
If the force \(\vec{F}=F_{x} \hat{i}+F_{y} \hat{j}\) is conservative then \(\dfrac{J F_{x}}{J y}=\dfrac{J F_{y}}{J x}\) For the force given in option (4) \(\begin{aligned}F_{x} & =x^{2} y^{3} \\\dfrac{J F_{x}}{J y} & =3 x^{2} y^{2} \\F_{y} & =y^{2} x^{3} \\\dfrac{J F_{y}}{J x} & =3 y^{2} x^{2} \\\Rightarrow \dfrac{J F_{x}}{J y} & =\dfrac{J F_{y}}{J x}\end{aligned}\) For the remaining forces the above condition is not fulfilled.
PHXI06:WORK ENERGY AND POWER
355398
Assertion : The work done by a conservative force such as gravity depends on the initial and final positions only. Reason : The work done by a force cannot be calculated if the nature of the force is not known.
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 work done by a force can be calculated sometimes even if the nature of the force is not known. Work done by conservative force depends on intial and final positions. So option (3) is correct.
355395
Work done by the conservative forces on a system is equal to
1 The change in kinetic energy of the system
2 The (\(-ve\)) of change in potential energy of the system
3 The (\(-ve\)) change in total mechanical energy of the system
4 None of the above
Explanation:
\(W=-\Delta U\)
PHXI06:WORK ENERGY AND POWER
355396
Assertion : Frictional forces are conservative forces. Reason : Potential energy can not be associated with frictional forces.
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:
For conservative force \(F\) there exists a function of potential energy \((U)\) such that magnitude of force is \(|F|=\dfrac{d U}{d r}\). Gravity and an electrostatic field in a vacuum are examples of conservative forces. However, any form of friction disrupts the field's conservativeness. Then, potential energy cannot be associated with frictional forces. So correct option is (4).
PHXI06:WORK ENERGY AND POWER
355397
Which of the following is a conservative force?
1 \(x y \hat{i}+4 \hat{j}\)
2 \(x y \hat{j}+x^{2} y^{2} \hat{j}\)
3 \(x^{2} y^{2} \hat{i}+x y \hat{j}\)
4 \(x^{2} y^{3} \hat{i}+y^{2} x^{3} \hat{j}\)
Explanation:
If the force \(\vec{F}=F_{x} \hat{i}+F_{y} \hat{j}\) is conservative then \(\dfrac{J F_{x}}{J y}=\dfrac{J F_{y}}{J x}\) For the force given in option (4) \(\begin{aligned}F_{x} & =x^{2} y^{3} \\\dfrac{J F_{x}}{J y} & =3 x^{2} y^{2} \\F_{y} & =y^{2} x^{3} \\\dfrac{J F_{y}}{J x} & =3 y^{2} x^{2} \\\Rightarrow \dfrac{J F_{x}}{J y} & =\dfrac{J F_{y}}{J x}\end{aligned}\) For the remaining forces the above condition is not fulfilled.
PHXI06:WORK ENERGY AND POWER
355398
Assertion : The work done by a conservative force such as gravity depends on the initial and final positions only. Reason : The work done by a force cannot be calculated if the nature of the force is not known.
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 work done by a force can be calculated sometimes even if the nature of the force is not known. Work done by conservative force depends on intial and final positions. So option (3) is correct.
355395
Work done by the conservative forces on a system is equal to
1 The change in kinetic energy of the system
2 The (\(-ve\)) of change in potential energy of the system
3 The (\(-ve\)) change in total mechanical energy of the system
4 None of the above
Explanation:
\(W=-\Delta U\)
PHXI06:WORK ENERGY AND POWER
355396
Assertion : Frictional forces are conservative forces. Reason : Potential energy can not be associated with frictional forces.
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:
For conservative force \(F\) there exists a function of potential energy \((U)\) such that magnitude of force is \(|F|=\dfrac{d U}{d r}\). Gravity and an electrostatic field in a vacuum are examples of conservative forces. However, any form of friction disrupts the field's conservativeness. Then, potential energy cannot be associated with frictional forces. So correct option is (4).
PHXI06:WORK ENERGY AND POWER
355397
Which of the following is a conservative force?
1 \(x y \hat{i}+4 \hat{j}\)
2 \(x y \hat{j}+x^{2} y^{2} \hat{j}\)
3 \(x^{2} y^{2} \hat{i}+x y \hat{j}\)
4 \(x^{2} y^{3} \hat{i}+y^{2} x^{3} \hat{j}\)
Explanation:
If the force \(\vec{F}=F_{x} \hat{i}+F_{y} \hat{j}\) is conservative then \(\dfrac{J F_{x}}{J y}=\dfrac{J F_{y}}{J x}\) For the force given in option (4) \(\begin{aligned}F_{x} & =x^{2} y^{3} \\\dfrac{J F_{x}}{J y} & =3 x^{2} y^{2} \\F_{y} & =y^{2} x^{3} \\\dfrac{J F_{y}}{J x} & =3 y^{2} x^{2} \\\Rightarrow \dfrac{J F_{x}}{J y} & =\dfrac{J F_{y}}{J x}\end{aligned}\) For the remaining forces the above condition is not fulfilled.
PHXI06:WORK ENERGY AND POWER
355398
Assertion : The work done by a conservative force such as gravity depends on the initial and final positions only. Reason : The work done by a force cannot be calculated if the nature of the force is not known.
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 work done by a force can be calculated sometimes even if the nature of the force is not known. Work done by conservative force depends on intial and final positions. So option (3) is correct.
