Question

A body is dropped from the roof of a multi storied building it passes the ceiling of the ${20}^{th}$ storey at a speed of $20m/s$, if the height of each storey is $5m$, then the number of storeys in the building.

• A. $24$
• B. $20$
• C. $25$
• D. $30$

Answer 1

Answer: (A)

$24$

Given,

$h=5m$ height of each storey

$u=0m/s$

$v=20m/s$ at the $20th$ storey

$g=10m/s^2$

Above the 20th storey, the height is d,

from 3rd equation of motion,

$v^2=u^2+2gd$

${20}^2=0+4gd$

$d=\frac{20\times 20}{2\times 10}=20m$

The no. of storey above the 20th storey is,

$n=\frac{d}{h}=\frac{20}{5}=4$

The total number of storey in the building is,

$n^{\prime }=20+4=24$

The correct option is A.