A smooth track of incline of length l is joined smoothly wi…

Physics Newton's Laws of Motion Mix MCQ (Single Correct)

A smooth track of incline of length l is joined smoothly with circular track of radius R. A mass of m kg is projected up from the bottom of the inclined plane. The minimum speed of the mass to reach the top of the track is given by, v =

[2g (I cos θ θ + R) (l + cos θ θ )] 1/2

(2g l sin θ θ + R) 1/2

[2g {1 sin θ θ + R (1 - cos θ θ )}] 1/2

(2glcos θ θ + R) 1/2

Text Solution

Verified by Experts

The correct answer is:

Using v 2 – u 2 = 2aS we get

v 2 – u 2 = 2(-g) H

i.e., - u 2 = 2(-g) (h 1 + h 2 )

but h 1 = l sin θ θ

and h 2 = R (1 – cos θ θ )

∴ ∴ u 2 = 2g (l sin θ θ + R (1 – cos θ θ ))

or u = [2g {l sin θ θ + R (1 – cos θ θ )}]

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