A trolley is falling freely on inclined plane as shown in the figure. The angle of string of the pendulum with the ceiling of trolley is (α) equal to

Given, angle of the inclined plane = θ

If T is the tension acting on the trolley,

The component of tension along the inclined plane is T cosα

And, if m is the mass of the system of trolley, then the component of weight along the inclined plane is mg sinθ

Now, in equilibrium the acceleration of the trolley will be equal to the acceleration of the bob

So, the net force along the plane will be

F = ma

mg sin θ + T cos α = ma

For a free falling trolley on an inclined plane, acceleration a = g sin θ

So, we have

mg sin θ + T cos α = mg sin θ

T cos α = 0

cos α = 0

α = 90o

Hence, the angle of string of pendulum with the coiling of trolley is 90o

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