Question

Which of the following is a true statement about the acceleration ~a of the pendulum bob

~a is equal to the acceleration due to gravity.
~a is perpendicular to the bob’s trajectory.

~a is equal to the instantaneous rate of change in velocity.
~a is tangent to the bob’s trajectory.

Answer 1

For a pendulum bob the motion is a part of circular motion which is under the influence of gravity

So here we will have two acceleration at any instant of time

1. Centripetal acceleration which will maintain the circular path

2. tangential acceleration which will change the magnitude of the speed

so here the net acceleration of the pendulum will be the vector sum of both accelerations

So we will say that net acceleration at any instant will give the instantaneous rate of change in the velocity.

so correct answer will be

a is equal to the instantaneous rate of change in velocity.