# 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)

Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Related Videos
Pseudo Force52 mins
Challenging Quiz on Newton Laws of Motion Part 364 mins
Pully Problems | Getting JEE Ready68 mins
Elaborative Lecture on Constraint Motion59 mins
Check your understanding of linear momentum22 mins
Why edges are raised for Curved roads? - Banking of roads54 mins
Into the world of springs - Spring force48 mins
Understand Newton's 2nd law Exhaustively34 mins
Basics strengthener - Newton Laws of motion61 mins
Escaping the reality - Concept of Pseudo Force54 mins
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
view all courses