Question

An object of mass '$m$' is kept on a horizontal platform. The platform is oscillating vertically with amplitude '$a$' and period '$T$'. The weight of object at lowest position is:

• A. $mg+ma{\omega }^2$
• B. $ma{\omega }^2$
• C. $mg$
• D. $mg-ma{\omega }^2$

Answer 1

Answer: (A)

$mg+ma{\omega }^2$

At the lowest point the acceleration of the particle is upwards (since the acceleration in SHM is towards the mean position), so the equation of motion is
$N-mg=ma{\omega }^2$
$N=$ normal force on the particle,

$a{\omega }^2$ is the acceleration in the SHM, at the extreme position.

Thus, weight of the particle is
$N=mg+ma{\omega }^2$