Question

A body rolls down a stair case of 5 steps. Each step has height 0.1 m and width 0.1 m. With what velocity will the body reach the bottom?

• A. $\sqrt{5/2}$ m/s
• B. $\left(1/\sqrt{2}\right)$ m/s
• C. $2\sqrt{2}$ m/s
• D. $5/\sqrt{2}$ m/s

Answer 1

The correct option is D $5/\sqrt{2}$ m/s

horzontal distance covered by the body = 5(0.1)

vertical distance covered by the body = 5(0.1)

if the time taken to hit the edge of 5th step is t ,then

5(0.1)=ut this eq$1$

5(0.1)= $\frac{1}{2}g{t}^2$ this is eq$2$

from1&2

5(0.1) = $\frac{1}{2}g[\frac{5\left(0.1\right)}{4}{]}^2$

$u^2=\frac{5\left(g\right)(0.1{)}^2}{2\left(0.1\right)}$

$u^2=\frac{5\left(10\right)\left(0.1\right)\left(0.1\right)}{2\left(0.1\right)}$

$u=\sqrt{\frac{5}{2}}\frac{m}{s}$