Assertion: The net work done by gravity is equal to the loss in the vertical component of the kinetic energy for a projectile.

Reason: The work-energy theorem applies to all systems including projectiles.

1. Both assertion and reason are true, and the reason is the correct explanation of the assertion.

2. Both assertion and reason are true, but the reason is not the correct explanation of the assertion.

3. Assertion is true but the reason is false.

4. Assertion is false but the reason is true.

Subtopic:  Work Energy Theorem |
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Given that $$\overrightarrow{F}=2\hat i+3\hat j$$ is force and $$\overrightarrow{r}=3\hat i-2\hat j$$ is the displacement position vector. Which of the following statements is correct?
1. Work done is zero, torque is 13 units
2. Work done is 13 units, torque is zero
3. Both work and torque are zero
4. Both work and torque are 13 units
Subtopic:  Work done by constant force |
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Statement I: Work done by friction is always negative.

Statement II: Kinetic friction is a non-conservative force.

1. Statement I is true, statement II is true and statement I is the correct reason for statement II.

2. Statement I is true, statement II is true, statement I is not the correct reason for statement II.

3. Statement I is true, statement II is false.

4. Statement I is false, statement II is true.

Statement II is true; Statement II is not the correct explanation of Statement IRead more on Sarthaks.com - https://www.sarthaks.com/196003/this-question-has-statement-and-statement-ii-the-four-choices-given-after-the-statement
Subtopic:  Concept of Work |
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Two billiard balls A and B, each of mass 50g and moving in opposite directions with a speed of 5 m/s each, collide and rebound at the same speed. If the collision lasts for ${10}^{-3}$ s,

(a) The impulse imparted to each ball is 0.25 $kg-m{s}^{-1}$ and the force on each ball is 250 N

(b) The impulse imparted to each ball is 0.25 $kg-m{s}^{-1}$ and the force exerted on each ball is 25 x N

(c) The impulse imparted to each ball is 0.5 N-s

(d) The impulse and the force on each ball are equal in magnitude and opposite in direction.

Which of the following statement(s) is/are true?

1. (a, c)

2. (a, b)

3. (c, d)

4. (b, c)

Subtopic:  Collisions |
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Two inclined frictionless tracks, one gradual and the other steep meet at A from where two stones are allowed to slide down from rest, one on each track as shown in the figure.

Which of the following statement is correct?

1. Both stones reach the bottom at the same time but not at the same speed.

2. Both the stones reach the bottom with the same speed and stone I reaches the bottom earlier than stone II.

3. Both the stones reach the bottom with the same speed and stone II reaches the bottom earlier than stone I.

4. Both stones reach the bottom at different times and at different speeds.

Subtopic:  Gravitational Potential Energy |
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A bullet of mass m fired at 300 to the horizontal leaves the barrel of the gun with a velocity v. The bullet hits a soft target at a height h above the ground while it is moving downward and emerge out with half the kinetic energy it had before hitting the target. Consider the following statements.

(a) The velocity of the bullet will be reduced to half its initial value.
(b) The velocity of the bullet will be more than half of its earlier velocity.
(c) The bullet will continue to move along the same parabolic path.
(d) The bullet will move in a different parabolic path.
(e) The bullet will fall vertically downward after hitting the target.
(f) The internal energy of the particles of the target will increase.

Which of the above-given statement(s) is/are correct in respect of the bullet after it emerges out of the target?
1. (a, c, f)

2. (a, d, f)

3. (b, d, f)

4. (a, b, c)

Subtopic:  Work Energy Theorem |
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The potential energy function for a particle executing linear simple harmonic motion is given by V(x) =$\frac{{\mathrm{kx}}^{2}}{2}$, where k is the force constant of the oscillator. For k = 0.5 N/m, the graph of V(x) versus x is shown in the figure. A particle of total energy 1 J moving under this potential must turn back when it reaches:

Subtopic:  Elastic Potential Energy |
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The figure shows the variation of the kinetic energy of a block of mass m connected to a spring. Kinetic energy at the extreme position for this block of mass m will be:

1. $k{x}_{m}^{2}$

2. $\frac{k{x}_{m}^{2}}{2}$

3. $\frac{k{x}_{m}^{2}}{4}$

4. Zero

Subtopic:  Elastic Potential Energy |
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A woman pushes a trunk on a railway platform that has a rough surface. She applies a force of 100 N over a distance of 10 m. Thereafter, she gets tired and her applied force reduces linearly with distance to 50 N. The total distance through which the trunk has been moved is 20 m. The plot of force applied by the woman and the frictional force, which is 50 N versus displacement is given below. Work done by frictional force over the first 10 m will be:

1.  -500 J

2.  500 J

3.  1000 J

4. -1000 J

Subtopic:  Work Energy Theorem |
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Assertion: Two particles moving in the same direction do not lose all their energy in a completely inelastic collision.
Reason: Principle of conservation of momentum holds true for all kinds of collisions.
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 and the reason is incorrect.
4. Assertion is incorrect and the reason is correct.
Subtopic:  Collisions |
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