Question

A section of fixed smooth circular track of radius R in vertical plane is shown in the figure. A block is released from position A and leaves the track at B. The radius of curvature of its trajectory when it just leaves the track at B is-

• A. R
• B. R/4
• C. R/2
• D. None

Answer 1

Answer: (C)

R/2

Answer 2

In figure

OC = R cos 53⁰ = $\frac{3R}{5}$; OE = R cos 37⁰ = $\frac{4R}{5}$

So CE = $\frac{R}{5}$

From A to B,

$\frac{1}{2}mv^{2}$= mg$\frac{R}{5}$ [Energy conservation]

v = $\sqrt{\frac{2gR}{5}}$

Let radius of curvature at B is r

g cos 37⁰ = $\frac{v^{2}}{r}$

r = $\frac{v^{2}}{g\cos 37º}$ = $\frac{2gR}{5 \times 10 \times 4/5}$ = $\frac{R}{2}$