Question

A marble rolls down from top of a staircase with constant horizontal velocity $u$.In each step is $y$ metre high and $x$ metre wide, the marble just hits the edge of the $n^{th}$ step when $n=$

• A. $\frac{x{u}^2}{g{y}^2}$
• B. $\frac{u^2}{gy}$
• C. $\frac{2y{u}^2}{g{x}^2}$
• D. $\frac{4y{u}^2}{g{x}^2}$

Answer 1

Answer: (C)

$\frac{2y{u}^2}{g{x}^2}$

Total horizontal distance to be covered $=x\times n=nx$
Total vertical distance to be covered $=y\times n=ny$
but $nx=ut$ and $ny=\frac{1}{2}g{t}^2$
so, $ny=\frac{1}{2}g{\left(\frac{nx}{u}\right)}^{2}orn=\frac{2y{u}^2}{g{x}^2}$