Question

A small block slides with velocity 0.5 √gr on the horizontal frictionless surface as shown in Fig. The block leaves the surface at L. The angle αis

• A. cos^-1$\frac{3}{4}$
• B. cos^-1 $\frac{4}{3}$
• C. sin^-1$\frac{3}{4}$
• D. sin^-1 $\frac{4}{3}$

Answer 1

Answer: (A)

cos^-1$\frac{3}{4}$

Answer 2

Here cos α = $\frac{r - h}{r}$

or -h = r cos α - r

or h = r(1 – cos α)

At L, mg cos α = $\frac{m}{r}v^{2}$

= $\frac{m}{r}\left\lbrack v_{0}^{2} + \left( \sqrt{2gh} \right)^{2} \right\rbrack$

or mg cos α = $\frac{m}{r}\left( \frac{1}{4}gr + 2gh \right)$

= $\frac{m}{r}\left( \frac{1}{4}gr + 2gh\left( 1 - \cos\alpha \right) \right)$

or cos A = $\frac{1}{4}$ + 2 – 2 cos α

or 3 cos α = $\frac{9}{4}$ or cos α = $\frac{3}{4}$

or α = cos^-1$\frac{3}{4}$