Question

Two plates A and B are placed one above the other in the gravitational field and a block of mass m is connected to the upper plate by a spring of spring constant k. Its time period is found to be T. Now the space between the plates is made gravity free and a charge $+q$ is given to the block of mass m and an electric field E is produced in the direction shown. The new time period is?

Answer 1

Two plates A and B are placed one above the other in the gravitation field.

Spring constant$=K$

Time period$=T$

Charge$=+q$

Mass$=m$

Electric field $=E$

New time period $=?$

Actually in equilibrium

$Kx=mg\\x=\cfrac{mg}{K}\\x=\cfrac{2mg}{K}$

When if it will dropped the block when the spring is in its natural length then block will go upto.

$T=2\pi \sqrt{\frac{x}{m}}=2\pi \sqrt{\frac{\frac{mg}{K}}{m}}=2\pi \sqrt{\frac{g}{K}}$