Read each statement below carefully and state, with reasons, if it is true or false:

**(a)** The net acceleration of a particle in a circular motion is always along the radius of the circle towards the centre.

**(b)** The velocity vector of a particle at a point is always along the tangent to the path of the particle at that point.

**(c) **The acceleration vector of a particle in uniform circular motion averaged over one cycle is a null vector.

Asked by Abhisek | 1 year ago | 86

**Right answer is (a) False**

**Explanation:-**

The net acceleration of a particle in a circular motion is always directed along the radius of the circle toward the centre only in the case of uniform circular motion.

**Right answer is (b) True**

**Explanation:-**

At a point on a circular path, a particle appears to move tangentially to the circular path.

**Right answer is (c) True**

**Explanation:-**

In uniform circular motion (UCM), the direction of the acceleration vector points toward the centre of the circle. However, it constantly changes with time. The average of these vectors over one cycle is a null vector.

Answered by Pragya Singh | 1 year ago**(a) **Show that for a projectile the angle between the velocity and the x-axis as a function of time is given by

\(\theta (t)=tan^{-1}(\dfrac{v_{0y-gt}}{v_{ox}})\)

**(b)** Shows that the projection angle θ_{0} for a projectile launched from the origin is given by

\(\theta_{0}=tan^{-1}(\dfrac{4h_{m}}{R})\)

where the symbols have their usual meaning

A cyclist is riding with a speed of 27 km/h. As he approaches a circular turn on the road of a radius of 80 m, he applies brakes and reduces his speed at the constant rate of 0.50 m/s every second. What is the magnitude and direction of the net acceleration of the cyclist on the circular turn?

A fighter plane flying horizontally at an altitude of 1.5 km with a speed of 720 km/h passes directly overhead an anti-aircraft gun. At what angle from the vertical should the gun be fired for the shell with muzzle speed 600 m s^{-1} to hit the plane? At what minimum altitude should the pilot fly the plane to avoid being hit? (Take g = 10 m s^{-2} ).

A bullet fired at an angle of 30° with the horizontal hits the ground 3.0 km away. By adjusting its angle of projection, can one hope to hit a target 5.0 km away? Assume the muzzle speed to be fixed, and neglect air resistance.

Can we associate a vector with

**(i)** a sphere

**(ii)** the length of a wire bent into a loop

**(iii)** a plane area

Clarify for the same.