Question

At an instant, a particle moving on a circular path has a velocity (2i +2j) m/s. The acceleration of the particle is (i +aj) m/s? at that instant. The particle's instantaneous tangential acceleration will be zero, if a is equal to​

Answer 1

value of a = -1

It has given that at an instant, a particle moving on a circular path has a velocity, v = (2i +2j) m/s. The acceleration of the particle , a_net = (i +aj) m/s? at that instant. The particle's instantaneous tangential acceleration will be zero.

we know, net acceleration of circular motion, a_net = radial acceleration + tangential acceleration

but here tangential acceleration is zero. so net acceleration is radial acceleration. but we know, radial acceleration is perpendicular on velocity of particle in circular path.

i.e., dot product of v and a_net = 0

⇒(2i + 2j).(i + a j) = 0

⇒2 + 2a = 0

⇒a = -1

therefore value of a = -1.