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

when 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.

but a charge +q is given to the block of mass m and an electric field E is produced in the downward direction as shown in figure.

at equilibrium,

spring force is balanced by electrostatic force

so, kd= Eq

we know, k = $m\omega^2$

so, $m\omega^2d=Eq$

or, $\omega^2=\frac{Eq}{md}$

or, $\omega=\sqrt{\frac{Eq}{md}}$

or,$T=2\pi\sqrt{\frac{md}{qE}}$

hence required time period is $\boxed{\bf{T=2\pi\sqrt{\frac{md}{qE}}}}$