A car is speeding up on a horizontal road with an acceleration a. Consider the following situations in the car. (i) A ball is suspended from the ceiling through a string and is maintaining a constant angle with the vertical. Find this angle. (ii) A block is kept on a smooth incline and does not slip on the incline. Find the angle of the incline with the horizontal.



Given: Let the pendulum (formed by the ball and the string) make angle θ with the vertical.


From the free-body diagram, Tcosθ − mg = 0


Tcosθ = mg


…i


ma − T sin θ = 0


⇒ ma = T sin θ


…. ii




So, the angle formed by the ball with the vertical is tan⁻ �[ a/g.]


(ii) Let the angle of the incline be θ. From the diagram,


⇒ ma cos θ = mg sin θ





So, the angle of incline is tan⁻ �(a/g)


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