Concepts Of Physics MCQ Edition [Volume 1]PhysicsNewton's Laws of Motion
A car accelerates on a horizontal road with an acceleration a . Two situations are considered inside the car. First, a ball is suspended from the ceiling by a string and maintains a constant angle with the vertical. Second, a block is placed on a smooth incline and does not slip on the incline. Determine the angle of the string with the vertical, and the angle of the incline with the horizontal.
Options
- A⁻¹ ( a g ) and ⁻¹ ( a g )
- B⁻¹ ( g a ) and ⁻¹ ( g a )
- C⁻¹ ( a g ) and ⁻¹ ( a g )
- D⁻¹ ( a g ) and ⁻¹ ( a g )
Correct answer
C. ⁻¹ ( a g ) and ⁻¹ ( a g )
Step-by-step solution
In the frame of the accelerating car, a pseudo force ma acts on the objects in the direction opposite to the acceleration. For the suspended ball, the forces acting are tension T , weight mg , and pseudo force ma . Resolving forces along the horizontal and vertical directions for equilibrium: T = ma T = mg Dividing the two equations, we get = a g = ⁻¹ ( a g ) . For the block on the smooth incline, the forces acting are normal reaction N , weight mg , and pseudo force ma . For the block to not slip, the net force al