Laws Of Motion

In a tug of war, if the two teams apply equal and opposite forces at each end of the rope, the rope is in equilibrium. This means that the tension in the rope is equal to the force applied by one of the teams. Since each team pulls with a force of 20 kN, the tension in the rope will be 20 kN, because the rope must resist this force to maintain equilibrium.

The correct option is (B) : 20kN

Contact forces are those that arise from physical contact between two objects, such as friction, air resistance, viscous force, and buoyant force. Gravitational force, on the other hand, is a non-contact force. It acts at a distance between objects with mass, such as between the Earth and an object on its surface.

The correct option is (E) : gravitational force

The center of mass speed of the system is given by the formula: Where:
,
,
(since the man is running opposite to the cart),
.
Substituting these values into the formula: Thus, the speed of the center of mass of the system is 0.2 ms .

The correct option is (C) :

Given:

• Mass of the box,
• Incline angle,
• Frictional force, (retarding motion)
• Box moves with constant speed (acceleration )
• Gravitational acceleration,

Step 1: Resolve Forces Along the Incline

The component of gravitational force along the incline is:

Step 2: Apply Equilibrium Condition

Since the box moves with constant speed, the net force along the incline is zero. Thus:

Here, is the horizontal force we need to find. Resolving it along the incline:

Conclusion:

The magnitude of the horizontal force is .

Answer:

Given:

• Five statements (A-E) about friction.

Step 1: Analyze Each Statement

(A) Static friction force is always equal to .

Incorrect. The static friction force is only equal to at its maximum value (when motion is impending). For other cases, static friction adjusts to match the applied force up to this maximum.

(B) Friction is a non-conservative force.

Correct. Friction dissipates energy as heat and depends on the path taken.

(C) Friction arises from electromagnetic force.

Correct. Friction results from microscopic interactions between surface atoms, which are electromagnetic in nature.

(D) Friction always opposes relative motion.

Correct. Kinetic friction opposes sliding, while static friction opposes the tendency to slide.

(E) Maximum static friction is .

Correct. This is the definition of the maximum static friction force.

Conclusion:

The incorrect statement is (A), as static friction equals only at its maximum.

Answer: