Question

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 =

• A. [2g(lcosθ + R)(l + cosθ)]^1/2
• B. (2g l sin θ + R)^1/2
• C. [2g{1 sinθ + R(1 - cosθ)}]^l/2
• D. (2glcosθ + R)^1/2

Answer 1

Answer: (C)

$2g{1 sinθ + R(1 - cosθ)}$^l/2

Answer 2

Using v² – u² = 2aS we get

v² – u² = 2(-g)H

i.e., - u²= 2(-g) (h₁ + h₂)

but h₁ = l sin θ

and h₂ = R(1 – cos θ)

∴ u² = 2g(l sin θ + R (1 – cos θ))

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