Questions On Centripetal Acceleration Class 11

Centripetal acceleration is a fundamental concept in circular motion, where an object moving in a circular path experiences acceleration directed toward the center of the circle. This acceleration is necessary to keep the object moving in a curved trajectory. In Class 11 Physics, understanding centripetal acceleration helps in solving problems related to motion in circular paths, such as planetary orbits, vehicle turns, and rotating systems.

This topic will cover important questions on centripetal acceleration, along with explanations and solutions, to help students grasp this topic effectively.

Table of Contents

What is Centripetal Acceleration?

Centripetal acceleration is the acceleration experienced by an object moving in a circular path. It always points toward the center of the circle and is given by the formula:

a_c = frac{v^2}{r}

where:

a_c = centripetal acceleration (m/s²)
v = velocity of the object (m/s)
r = radius of the circular path (m)

Centripetal acceleration occurs because an object in circular motion continuously changes its direction, even if its speed remains constant.

Basic Questions on Centripetal Acceleration

Q1: What is the direction of centripetal acceleration?

Answer: Centripetal acceleration always acts toward the center of the circular path.

Q2: Does centripetal acceleration change the speed of an object?

Answer: No, centripetal acceleration changes only the direction of velocity, not its magnitude.

Q3: What happens if centripetal acceleration is removed?

Answer: If centripetal acceleration is removed, the object will move in a straight line due to inertia, following Newton’s First Law of Motion.

Numerical Questions on Centripetal Acceleration

Q4: A car is moving in a circular track of radius 50 m with a speed of 10 m/s. Find its centripetal acceleration.

Solution:
Given:
v = 10 m/s,
r = 50 m

Using the formula:

a_c = frac{v^2}{r}

a_c = frac{10^2}{50} = frac{100}{50} = 2 text{ m/s²}

Answer: The centripetal acceleration is 2 m/s².

Q5: A cyclist turns on a circular track of radius 20 m at a speed of 5 m/s. Calculate the centripetal acceleration.

Solution:
Given:
v = 5 m/s,
r = 20 m

Using the formula:

a_c = frac{v^2}{r}

a_c = frac{5^2}{20} = frac{25}{20} = 1.25 text{ m/s²}

Answer: The centripetal acceleration is 1.25 m/s².

Conceptual Questions on Centripetal Acceleration

Q6: Why do astronauts feel weightless in an orbiting spacecraft?

Answer: In an orbiting spacecraft, both the astronaut and the spacecraft are in free fall due to centripetal acceleration provided by gravity. Since they fall at the same rate, astronauts experience weightlessness.

Q7: Can an object have centripetal acceleration without a force acting on it?

Answer: No, centripetal acceleration requires a net force (centripetal force) directed toward the center. Without this force, the object would move in a straight line due to inertia.

Advanced Questions on Centripetal Acceleration

Q8: Derive the formula for centripetal acceleration.

Derivation:
Centripetal acceleration is given by:

a_c = frac{v^2}{r}

We know that velocity in a circular motion is given by:

v = r omega

where omega is the angular velocity. Substituting this in the centripetal acceleration formula:

a_c = frac{(r omega)^2}{r} = r omega^2

Thus, we get an alternative formula:

a_c = r omega^2

This formula shows that centripetal acceleration is also dependent on angular velocity.

Q9: A satellite orbits Earth at a radius of 7000 km with a velocity of 7500 m/s. Calculate its centripetal acceleration.

Solution:
Given:
v = 7500 m/s,
r = 7000 km = 7,000,000 m

Using the formula:

a_c = frac{v^2}{r}

a_c = frac{(7500)^2}{7,000,000}

a_c = frac{56,250,000}{7,000,000} = 8.04 text{ m/s²}

Answer: The centripetal acceleration is 8.04 m/s².

Q10: A ball is tied to a string and whirled in a horizontal circle. If the tension in the string is 20 N and the mass of the ball is 2 kg, find the centripetal acceleration.

Solution:
Using Newton’s Second Law:

F = m a_c

Given:
F = 20 N,
m = 2 kg

a_c = frac{F}{m} = frac{20}{2} = 10 text{ m/s²}

Answer: The centripetal acceleration is 10 m/s².

Common Misconceptions About Centripetal Acceleration

Centripetal acceleration means increasing speed – False. It changes direction, not speed.
Objects moving in a circle must have an outward force – False. The force is always inward, not outward.
Centripetal acceleration applies only to cars and planets – False. It applies to any circular motion, including atoms and spinning rides.

Real-Life Applications of Centripetal Acceleration

Turning a Car: When a car takes a turn, friction between the tires and road provides centripetal force, causing the required acceleration.
Artificial Gravity in Space: Space stations create artificial gravity by rotating, using centripetal acceleration.
Roller Coasters: The loops in roller coasters require precise calculations of centripetal acceleration to ensure safety.
Earth’s Orbit Around the Sun: The gravitational force between the Earth and the Sun acts as centripetal force, keeping Earth in orbit.

Centripetal acceleration is a crucial concept in circular motion, ensuring that objects follow curved paths. It plays an important role in physics, engineering, and even everyday life, from vehicles on roads to satellites in space.

By understanding its principles and solving questions related to it, students can master this topic in Class 11 Physics. Whether it’s numerical problems, conceptual questions, or real-world applications, centripetal acceleration is a fascinating and essential area of study.