Question 1:
easyA cyclist is moving with speeding up itself in a circular track then work done by net force on cyclist will be :
As the speed of cyclist is increasing positive tangential acceleration is acting on the object. so net acceleration makes an acute angle with velocity.
As, net acceleration and net force will have same direction, angle between velocity and net force is acute. Work done will be positive.
Question 2:
easyAssertion (A): A particle moving at constant speed and constant magnitude of radial acceleration must be undergoing uniform circular motion.
Reason (R): In uniform circular motion speed cannot change as there is no tangential acceleration.
Assertion (A): Constant speed and constant magnitude of radial acceleration ((v^2/r)) imply constant radius ((r)), which defines uniform circular motion. So (A) is True.
Reason (R): In uniform circular motion, acceleration is purely centripetal (radial), with no component tangential to the path. Thus, speed remains constant. So (R) is True.
Reason (R) correctly explains why constant speed and constant radial acceleration magnitude lead to uniform circular motion by implying constant radius and absence of tangential acceleration.
Question 3:
easyAssertion (A): A particle is moving in a circle with constant tangential acceleration such that its speed \(v\) is increasing. Angle made by resultant acceleration of the particle with tangential acceleration increases with time.
Reason (R): Tangential acceleration \(= |dv/dt|\) and centripetal acceleration \(= v^2/R\).
With constant tangential acceleration \(a_t\) and increasing speed \(v\), centripetal acceleration \(a_c = v^2/R\) increases. The angle \(phi\) between resultant and tangential acceleration follows \(tan\phi = a_c/a_t\), so \(\phi\) increases. Thus (A) is true. (R) correctly defines these accelerations, providing the basis for (A).
Question 4:
easyAssertion (A): The equation of motion can be applied only if the acceleration is along the direction of velocity and is constant.
Reason (R): In circular motion, if velocity is constant then its motion is called uniform circular motion.
Equations of motion (kinematic equations) are for constant acceleration, irrespective of its direction relative to velocity. So (A) is false. In uniform circular motion, speed is constant, but velocity (a vector) continuously changes direction, hence it is not constant. So (R) is false. Both are false.
Question 5:
easyAssertion (A): In non-uniform circular motion, linear speed of the body is variable.
Reason (R): In non-uniform circular motion, acceleration of the body is towards the centre.
In non-uniform circular motion, linear speed is variable, so (A) is true. The net acceleration has both radial (centripetal) and tangential components, so it's not solely towards the center. Thus, (R) is false.
Question 6:
easyAssertion (A): A body is moving along a circle with a variable angular speed. Work done by centripetal force will be zero.
Reason (R): In non-uniform circular motion, net force on the body is not in the radial direction.
Centripetal force is always perpendicular to displacement, so work done by it is zero. Thus, (A) is true. In non-uniform circular motion, a tangential force exists, so the net force is not purely radial. Thus, (R) is true. However, (R) does not explain (A).