If an object is moving on a curved path, then
which of the following physical quantities may be
constant during the motion? (symbols have usual
meanings)

(1) only

Explanation:

Let's analyze each option.

(1)

this quantity corresponds to the rate of change of the module of the velocity, so it is basically the magnitude of the acceleration. In a uniform circular motion, the magnitude of the (centripetal) acceleration is

where v is the speed and r the radius: since both v and r can be constant, then this means that this quantity can be constant as well.

(2) (vector)

This quantity is the velocity. Velocity is a vector: this means it has both a magnitude (the speed) and a direction. In a uniform circular motion, the speed can be constant; however, we know that the direction is for sure not constant, since the object is constantly changing path: therefore, this quantity cannot be constant.

(3) (vector)

This quantity is the acceleration. Acceleration is a vector: this means it has both a magnitude (given by ) and a direction. In a uniform circular motion, the direction of the (centripetal) acceleration is towards the centre of the circle, perpendicular to the velocity: however, since the object is constantly changing direction, this means that also the direction of the acceleration is constantly changing, therefore this quantity cannot be constant.

the displacement produced by the body.  

the amount of force subjected to the body.  

the angle between the direction of force and displacement