One of the greatest physics experiments in history measured the charge-to-mass r

Question

One of the greatest physics experiments in history measured the charge-to-mass ratio of an electron, q/m. If a uniform potential difference is created between two plates, atomized particles---each with an integral amount of charge---can be suspended in space. The assumption is that the particles of unknown mass, M, contain a net number, n, of electrons of mass m and charge q. For a plate separation of d, what is the potential difference necessary to suspend a particle of mass M containing n net electrons? (Assume that M » m. Use any variable or symbol stated above along with the following as necessary: g.)
?V =
What is the acceleration of the particle if the voltage is cut in half? (Indicate an upward acceleration with a positive sign, and a downward acceleration with a negative sign. Use any variable or symbol stated above along with the following as necessary: g.)
a =
What is the acceleration of the particle if the voltage is doubled (Use any variable or symbol stated above along with the following as necessary: g.)
a =

Explanation / Answer

Here     weight is balenced by      qV /d Mg   = qV /d     ...........(1) Here d = distave between the plates   , V = applied voltage q = ne     total charge of the n nuber of electrons Applied potential    V   = mgd / ne   --------------------------------- If   the potential differece is   cut in half     V /2 qV /2d      =Ma   Here a = accelaration of the particle (1/2)qV /d   = Ma from equation (1) (1/2) Mg   = Ma a    =   g /2   --------------------------------------------- If   the potential difference   is    V' = 2V qV ' /d      =Ma     ==>   q(2V ) / d    = Ma 2 (qV /d ) = Ma   2 ( Mg )   = Ma a   = 2g qV ' /d qV ' /d      =Ma     ==>   q(2V ) / d    = Ma 2 (qV /d ) = Ma   2 ( Mg )   = Ma a   = 2g

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