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PHXI06:WORK ENERGY AND POWER

355399 Assertion :
Work done in moving a body over a closed loop is zero for every force in nature.
Reason :
Work done depends on whether force is conservative or non conservative.(around round-trip)

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.

PHXI06:WORK ENERGY AND POWER

355400 Which of the following statements are correct?
$A$ . If a particle moves opposite to the conservative field, potential energy will increase
$B$ . If a particle moves in the direction of conservative field, the potential energy will increase
$C$ . If a particle moves opposite to the conservative field, work done by the field will be positive
$D$ . If a particle moves opposite to the conserv ative field, work done by the field will be negative

1

A, C

2

A, D

3

B, C

4

B, D

PHXI06:WORK ENERGY AND POWER

355401 Assertion :
Work done by or against gravitational force in moving a body from one point to another is independent of the actual path followed between the two points.
Reason :
Gravitational forces are conservative 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.

PHXI06:WORK ENERGY AND POWER

355402 $F = 2 x^{2} - 3 x - 2$ . Choose correct option

1

x = - 1 / 2

is a position of stable equilibrium

2

x = 2

is a position of stable equilibrium

3

x = - 1 / 2

is a position of unstable equilibrium

4

x = 2

is a position of natural equilibrium

Explanation:

For equilibrium, $F = 0$
So $0 = 2 x^{2} - 3 x - 2 \Rightarrow 0 = 2 x^{2} - 4 x + x - 2$
$0 = 2 x (x - 2) + 1 (x - 2) \Rightarrow x = 2, \frac{- 1}{2}$
For checking nature of equilibrium.
$\begin{aligned} \frac{d^{2} U}{d x^{2}} = \frac{d}{d x} [\frac{d U}{d x}] = \frac{d}{d x} [- F] = \frac{d}{d x} [- 2 x^{2} + 3 x + 2] \\ \frac{d^{2} U}{d x^{2}} = - 4 x + 3 \end{aligned}$
At $x = 2, \frac{d^{2} U}{d x^{2}} = - 5$ Unstable equilibrium
At $x = - \frac{1}{2}, \frac{d^{2} U}{d x^{2}} = + 5$ Stable equilibrium

PHXI06:WORK ENERGY AND POWER

355399 Assertion :
Work done in moving a body over a closed loop is zero for every force in nature.
Reason :
Work done depends on whether force is conservative or non conservative.(around round-trip)

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.

PHXI06:WORK ENERGY AND POWER

355400 Which of the following statements are correct?
$A$ . If a particle moves opposite to the conservative field, potential energy will increase
$B$ . If a particle moves in the direction of conservative field, the potential energy will increase
$C$ . If a particle moves opposite to the conservative field, work done by the field will be positive
$D$ . If a particle moves opposite to the conserv ative field, work done by the field will be negative

1

A, C

2

A, D

3

B, C

4

B, D

PHXI06:WORK ENERGY AND POWER

355401 Assertion :
Work done by or against gravitational force in moving a body from one point to another is independent of the actual path followed between the two points.
Reason :
Gravitational forces are conservative 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.

PHXI06:WORK ENERGY AND POWER

355402 $F = 2 x^{2} - 3 x - 2$ . Choose correct option

1

x = - 1 / 2

is a position of stable equilibrium

2

x = 2

is a position of stable equilibrium

3

x = - 1 / 2

is a position of unstable equilibrium

4

x = 2

is a position of natural equilibrium

Explanation:

For equilibrium, $F = 0$
So $0 = 2 x^{2} - 3 x - 2 \Rightarrow 0 = 2 x^{2} - 4 x + x - 2$
$0 = 2 x (x - 2) + 1 (x - 2) \Rightarrow x = 2, \frac{- 1}{2}$
For checking nature of equilibrium.
$\begin{aligned} \frac{d^{2} U}{d x^{2}} = \frac{d}{d x} [\frac{d U}{d x}] = \frac{d}{d x} [- F] = \frac{d}{d x} [- 2 x^{2} + 3 x + 2] \\ \frac{d^{2} U}{d x^{2}} = - 4 x + 3 \end{aligned}$
At $x = 2, \frac{d^{2} U}{d x^{2}} = - 5$ Unstable equilibrium
At $x = - \frac{1}{2}, \frac{d^{2} U}{d x^{2}} = + 5$ Stable equilibrium

PHXI06:WORK ENERGY AND POWER

355399 Assertion :
Work done in moving a body over a closed loop is zero for every force in nature.
Reason :
Work done depends on whether force is conservative or non conservative.(around round-trip)

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.

PHXI06:WORK ENERGY AND POWER

355400 Which of the following statements are correct?
$A$ . If a particle moves opposite to the conservative field, potential energy will increase
$B$ . If a particle moves in the direction of conservative field, the potential energy will increase
$C$ . If a particle moves opposite to the conservative field, work done by the field will be positive
$D$ . If a particle moves opposite to the conserv ative field, work done by the field will be negative

1

A, C

2

A, D

3

B, C

4

B, D

PHXI06:WORK ENERGY AND POWER

355401 Assertion :
Work done by or against gravitational force in moving a body from one point to another is independent of the actual path followed between the two points.
Reason :
Gravitational forces are conservative 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.

PHXI06:WORK ENERGY AND POWER

355402 $F = 2 x^{2} - 3 x - 2$ . Choose correct option

1

x = - 1 / 2

is a position of stable equilibrium

2

x = 2

is a position of stable equilibrium

3

x = - 1 / 2

is a position of unstable equilibrium

4

x = 2

is a position of natural equilibrium

Explanation:

For equilibrium, $F = 0$
So $0 = 2 x^{2} - 3 x - 2 \Rightarrow 0 = 2 x^{2} - 4 x + x - 2$
$0 = 2 x (x - 2) + 1 (x - 2) \Rightarrow x = 2, \frac{- 1}{2}$
For checking nature of equilibrium.
$\begin{aligned} \frac{d^{2} U}{d x^{2}} = \frac{d}{d x} [\frac{d U}{d x}] = \frac{d}{d x} [- F] = \frac{d}{d x} [- 2 x^{2} + 3 x + 2] \\ \frac{d^{2} U}{d x^{2}} = - 4 x + 3 \end{aligned}$
At $x = 2, \frac{d^{2} U}{d x^{2}} = - 5$ Unstable equilibrium
At $x = - \frac{1}{2}, \frac{d^{2} U}{d x^{2}} = + 5$ Stable equilibrium

PHXI06:WORK ENERGY AND POWER

355399 Assertion :
Work done in moving a body over a closed loop is zero for every force in nature.
Reason :
Work done depends on whether force is conservative or non conservative.(around round-trip)

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.

PHXI06:WORK ENERGY AND POWER

355400 Which of the following statements are correct?
$A$ . If a particle moves opposite to the conservative field, potential energy will increase
$B$ . If a particle moves in the direction of conservative field, the potential energy will increase
$C$ . If a particle moves opposite to the conservative field, work done by the field will be positive
$D$ . If a particle moves opposite to the conserv ative field, work done by the field will be negative

1

A, C

2

A, D

3

B, C

4

B, D

PHXI06:WORK ENERGY AND POWER

355401 Assertion :
Work done by or against gravitational force in moving a body from one point to another is independent of the actual path followed between the two points.
Reason :
Gravitational forces are conservative 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.

PHXI06:WORK ENERGY AND POWER

355402 $F = 2 x^{2} - 3 x - 2$ . Choose correct option

1

x = - 1 / 2

is a position of stable equilibrium

2

x = 2

is a position of stable equilibrium

3

x = - 1 / 2

is a position of unstable equilibrium

4

x = 2

is a position of natural equilibrium

Explanation:

For equilibrium, $F = 0$
So $0 = 2 x^{2} - 3 x - 2 \Rightarrow 0 = 2 x^{2} - 4 x + x - 2$
$0 = 2 x (x - 2) + 1 (x - 2) \Rightarrow x = 2, \frac{- 1}{2}$
For checking nature of equilibrium.
$\begin{aligned} \frac{d^{2} U}{d x^{2}} = \frac{d}{d x} [\frac{d U}{d x}] = \frac{d}{d x} [- F] = \frac{d}{d x} [- 2 x^{2} + 3 x + 2] \\ \frac{d^{2} U}{d x^{2}} = - 4 x + 3 \end{aligned}$
At $x = 2, \frac{d^{2} U}{d x^{2}} = - 5$ Unstable equilibrium
At $x = - \frac{1}{2}, \frac{d^{2} U}{d x^{2}} = + 5$ Stable equilibrium

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