Question

A person weighing $60kg$ stands on a platform which oscillates up and down at a frequency of $2Hz$ and amplitude $5cm$. The maximum and minimum apparent weights are nearly: ($g$ = 10$m/s^2$)

• A. $108$ kg-wt, $12$ kg-wt
• B. $108$ kg-wt, $24$ kg-wt
• C. $54$ kg-wt, $12$ kg-wt
• D. $54$ kg-wt, $24$ kg-wt

Answer 1

The correct option is A $108$ kg-wt, $12$ kg-wt

$a={\omega }^{2}x$
So, $a_{max}=$ ${\omega }^{2}A$
We know that $\omega =2\pi f$
So, $a_{max}=\frac{(2\pi \times 2{)}^2\times 5}{100}$
Case I:
$N-mg=m{a}_{max}$
$N=m(a_{max}+g)$
$=60(10+\frac{16\times {\pi }^2\times 5}{100})$
$=1080$

$N=108$ kg-wt

Case II:
$mg-N=m{a}_{max}$
or, $N=mg-m{a}_{max}$
$=60(10-8)$
$=120N=12$ kg-wt