These questions consist of two statements each printed as assertion an...
Non-Uniform Circular Motion
Assertion: In a non-uniform circular motion, the acceleration of the particle is equal to the sum of the tangential acceleration and the centripetal acceleration.
Reason: The two accelerations are perpendicular to each other.
Explanation:
Non-uniform circular motion refers to a motion of a particle in a circular path with varying speed. In this type of motion, the velocity of the particle changes continuously, and hence there is an acceleration acting on the particle. The two types of acceleration acting on the particle are tangential acceleration and centripetal acceleration.
Tangential acceleration is the acceleration acting tangentially to the circular path and is responsible for the change in the magnitude of the velocity of the particle. Centripetal acceleration is the acceleration acting towards the center of the circular path and is responsible for the change in the direction of the velocity of the particle.
The assertion states that in non-uniform circular motion, the acceleration of the particle is equal to the sum of the tangential acceleration and the centripetal acceleration. This is true as both the accelerations act on the particle simultaneously and are perpendicular to each other.
The reason given for the assertion is that the two accelerations are perpendicular to each other. This is also true as the tangential acceleration acts along the tangent to the circular path while the centripetal acceleration acts along the radius of the circular path towards the center. Hence, the two accelerations are perpendicular to each other.
Therefore, the correct answer is option 'D' - Assertion is false but reason is true. The reason explains the concept of the two types of acceleration acting on a particle in non-uniform circular motion. However, the assertion is not true as the acceleration of the particle is not equal to the sum of the tangential acceleration and the centripetal acceleration, but rather it is the vector sum of the two accelerations.
These questions consist of two statements each printed as assertion an...
(D) because in non uniform circular motion acceleration is not the algebraic sum of tangential and centripetal acceleration but it is the vector sum of centripetal and tangential acceleration. and yes also both tangential and centripetal acceleration are always perpendicular to each other.