Question

Assertion and Reason are given in following questions. Each question have four option. One of them is correct it. (1) If both assertion and reason and the reason is the correct explanation of the Assertion. (2) If both assertion and reason are true but reason is not the correct explanation of the assertion. (3) If the assertion is true but reason is false. (4) If the assertion and reason both are false. Assertion: Work done by centripetal force is zero. Reason: This is because centripetal force is always along the tangent. (A)1 (B) 2 (C) 3 (D) 4

Short answer

The answer is (C) 3. The assertion is true as the work done by centripetal force is zero, but the reason is false because centripetal force is not always along the tangent, it acts towards the center of a circular path.

Step-by-step solution

We are given the assertion that the work done by centripetal force is zero. To analyze this assertion, we need to remember the formula for work done: W = F * d * cos(θ), where W is the work done, F is the force applied, d is the distance covered, and θ is the angle between force and displacement. #Step 2: Understand the reason#

The reason provided is that centripetal force is always along the tangent. This statement is false. The centripetal force acts towards the center of a circular path. The direction of the force is thus perpendicular to the tangent. #Step 3: Verify the truth of the assertion#

Since we know the formula for work done and that centripetal force acts towards the center of a circular path, we can verify the truth of the assertion. In the case of centripetal force, θ is 90° due to the force being perpendicular to the tangent. The cosine of 90° is 0, so the work done (W) is 0 as well. This verifies the assertion to be true. #Step 4: Choose the correct option#

Now that we have found the assertion to be true and the reason to be false, we can select the correct option. Option (C) states that the assertion is true and the reason is false, so our answer is (C) 3.

Key concepts

Centripetal Force

Centripetal force is a fundamental concept in physics, especially when dealing with objects moving in a circular path. This force always points toward the center of the circle and is necessary for an object to maintain its circular motion.

When something moves in a circle, even at constant speed, it is accelerating because its direction changes constantly. This acceleration is called centripetal acceleration, and it is caused by centripetal force.

The formula to calculate centripetal force is: \[ F_c = \frac{mv^2}{r} \]

• \( F_c \) is the centripetal force,
• \( m \) is the mass of the object,
• \( v \) is the velocity of the object,
• \( r \) is the radius of the circular path.

If the force points outward, it's not a centripetal force. For example, the tension in a string pulling a twirling ball or gravitational force keeping the moon in orbit are classic examples of centripetal force. Without this force, objects would move in straight lines, not circles.

Work Done in Physics

In physics, work is defined as the product of the force applied on an object and the distance over which it is applied. The important aspect of calculating work is the angle between the force and the direction of motion. The formula is:\[ W = F \cdot d \cdot \cos(\theta) \]

• \( W \) is the work done,
• \( F \) is the force applied,
• \( d \) is the displacement caused by the force,
• \( \theta \) is the angle between the force direction and displacement.

Work becomes zero when the force is perpendicular to the displacement (\( \theta = 90° \)). This is why the work done by a centripetal force is zero, as it is always perpendicular to the motion direction. Keep in mind, if the object moves in a circle, the displacement in the direction of applied force over one complete circle is zero.

Understanding Forces in Circular Motion

Forces acting on an object in circular motion can often be misunderstood. The key idea here is understanding how centripetal force functions in maintaining circular motion.

Consider a car taking a circular turn on a road. The friction between the car's tires and the road acts as the centripetal force, allowing the car to maintain its circular path.

It's important to remember:

• Centripetal force is not a new type of force, but a role played by other forces, like tension, gravity, or friction.
• If the centripetal force fails, the object will continue straight, not curve, due to inertia.
• The centripetal force never acts along the path of the object.

This perfect alignment inward avoids any net work being done, as seen in our previous section, ensuring that energy remains constant in uniform circular motion. Such understanding helps clear common misconceptions regarding circular motion and forces involved.